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Using identities, evaluate 71²

Answer: 5041 712 can be written as (70 + 1)2 ∴ 712 = (70 + 1)2 Using the identity (a + b)2 = a2 + b2 + 2ab (70 + 1)2 = (70)2 + 12 + 2... View Article

Using identities, evaluate 78 x 82

Answer: 6396 78 can be written as (80 - 2) and 82 can be written as (80 + 2) 78 x 82 = (80 - 2)(80 + 2) Using the identity (a + b)(a - b) = a2... View Article

Using identities, evaluate 8.9²

Answer: 79.21 8.92 can be written as (9 - 0.1)2 8.92 = (9 - 0.1)2 (a - b)2 = a2 + b2 - 2ab (9 - 0.1)2 = 92 + 0.12 - 2 × 9 × 0.1 (9... View Article

Using identities, evaluate 99²

Answer: 9801 992 can be written as (100 - 1)2 ∴ 992 = (100 - 1)2 Using the identity (a - b)2 = a2 + b2 - 2ab (100 - 1)2= (100)2 + 12 - 2... View Article

Using identities, evaluate 998²

Answer: 996004 9982 can be written as (1000 - 2)2 Using the identity (a - b)2 = a2 + b2 - 2ab (998)2 = (1000 – 2)2 (1000 - 2)2 = 10002 +... View Article

Verify that: -(-x) = x for. (i) x = 11/15 (ii) x = -13/17

Answer: Given -(-x) = x (i) x = 11/15 We have, x = 11/15 An additive inverse of a number is defined as the value, which on adding with the... View Article

Verify that: x³ + y³ + z³ – 3xyz = (1/2) (x + y + z)[(x – y)² + (y – z)² + (z – x)²]

Answer: Given x3 + y3 + z3 - 3xyz = (1/2) (x + y + z)[(x - y)2 + (y - z)2 + (z - x)2] LHS = x3 + y3 + z3 - 3xyz RHS = (1/2) (x + y + z)[(x - y)2... View Article

Verify whether the following are zeroes of the polynomial, indicated against them: p(x) = (x+1)(x–2), x = −1, 2

Answer: A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest... View Article

Verify whether the following are zeroes of the polynomial, indicated against them: p(x) = 3x + 1, x= −1/3

Answer: A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the... View Article

Verify whether the following are zeroes of the polynomial, indicated against them: p(x) = 3x² −1, x = -1/√3 , 2/√3

Answer: A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest... View Article

Verify whether the following are zeroes of the polynomial, indicated against them: p(x) = 5x – π, x = 4/5

Answer: A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the... View Article

Verify whether the following are zeroes of the polynomial, indicated against them: p(x) = lx + m, x = −m/l

Answer: A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest... View Article

Verify whether the following are zeroes of the polynomial, indicated against them: p(x) = x², x = 0

Answer: A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest... View Article

Verify whether the following are zeroes of the polynomial, indicated against them: p(x) = x² −1, x=1, −1

Answer: A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the... View Article

Verify whether the following are zeroes of the polynomial, indicated against them: p(x) =2x + 1, x = 1/2

Answer: A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest... View Article

Verify: x^{3 – y³ = (x – y)(x² + xy + y²)}

Answer: Given x3 - y3 = (x - y)(x2 + xy + y2) In the given equation LHS = x3 - y3 RHS = (x - y)(x2 + xy + y2) Consider LHS x3 - y3 We know... View Article

Verify: x³ + y³ = (x + y)(x² – xy + y²)

Answer: Given x3 + y3 = (x + y)(x2 - xy + y2) (x + y)3 = x3 + y3 + 3xy(x + y) In the given equation LHS = x3 + y3 RHS = (x + y)(x2 - xy + y2)... View Article

Wastewater released by houses is called ____________.

Answer: Wastewater released by houses is called sewage. Sewage is actually the wastewater that is released from houses, hospitals, industries,... View Article

We can see a non-luminous object when light: (a) emitted by the object falls on the eye. (b) is reflected from the object towards our eye. (c) completely passes through the object. (d) gets completely absorbed by the object.

Answer: (b) is reflected from the object towards our eye. We can see a non-luminous object when light reflected by the object enters our eyes.... View Article

We have a stringed musical instrument. The string is plucked in the middle first with a force of greater magnitude and then with a force of smaller magnitude. In which case would the instrument produce a louder sound?

Answer: The amplitude of vibration determines the loudness of the sound. When a string is plucked with greater force amplitude of string will be... View Article

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