Archives

Using (x + a) (x + b) = x² + (a + b) x + ab, find (5.1 x 5.2)

Answer: 26.52 5.1 x 5.2 can be written as (5 + 0.1)(5 + 0.2) 5.1 x 5.2 = (5 + 0.1) × (5 + 0.2) Using (x + a)(x + b) = x2 + (a + b) x + ab... View Article

Using (x + a) (x + b) = x² + (a + b) x + ab, find 103 x 98

Answer: 10094 103 x 98 can be written as (100 + 3)(100 + (-2)) 103 x 98 = (100 + 3)(100 + (-2)) Using (x + a)(x + b) = x2 + (a + b) x + ab... View Article

Using (x + a) (x + b) = x² + (a + b) x + ab, find 9.7 x 9.8

Answer: 95.06 9.7 x 9.8 can be written as (9 + 0.7 )(9 + 0.8) 9.7 x 9.8 = (9 + 0.7 )(9 + 0.8) Using (x + a)(x + b) = x2 + (a + b) x + ab... View Article

Using a² – b² = (a + b)(a – b), find (i) 153² – 147² (ii) 12.1² – 7.9²

Answer: 1800 Using the identity a2 - b2 = (a + b)(a - b) 1532 - 1472 Put a = 153 b = 147 1532 - 1472= (153 + 147)(153 - 147) 1532 - 1472= 300... View Article

Using a² – b² = (a + b)(a – b), find (i) 51² – 49² (ii) (1.02)² – (0.98)²

Answer: Using the identity a2 - b2 = (a + b)(a - b) 512 - 492 Put a = 51 b = 49 512 - 492 = (51 + 49)(51 - 49) 512 - 492 = 100 × 2... View Article

Using appropriate properties find: -2/3 × 3/5 + 5/2 – 3/5 × 1/6

Answer: -2/3 × 3/5 + 5/2 - 3/5 × 1/6 By commutativity ⇒ -2/3 × 3/5 - 3/5 × 1/6 + 5/2 Commutative property - As per... View Article

Using appropriate properties find: 2/5 × (- 3/7) – 1/6 × 3/2 + 1/14 × 2/5

Answer: 2/5 × (-3/7) - 1/6 × 3/2 + 1/14 × 2/5 By commutativity ⇒ 2/5 × (-3/7) + 1/14 × 2/5 - (1/6 × 3/2)... View Article

Using identities, evaluate 10.5 x 9.5

Answer: 99.75 10.5 can be written as (10 + 0.5) and 9.5 can be written as (10 - 0.5) 10.5 x 9.5 = (10 + 0.5)(10 - 0.5) (10 + 0.5)(10 - 0.5) =... View Article

Using identities, evaluate 102²

Answer: 10404 1022 can be written as (100 + 2)2 1022 = (100 + 2)2 Using the identity (a + b)2 = a2 + b2 + 2ab 1022 = (100 + 2)2 (100 + 2)2 =... View Article

Using identities, evaluate 297 x 303

Answer: 89991 297 can be written as (300 - 3) and 303 can be written as (300 + 3) 297 x 303 = (300 - 3) × (300 + 3) Using the identity (a... View Article

Using identities, evaluate 5.2²

Answer: 27.4 5.22 can be written as (5 + 0.2)2 Using the identity (a + b)2 = a2 + b2 + 2ab 5.22 = (5 + 0.2)2 (5 + 0.2)2 = 52 + 0.22 + 2 ×... View Article

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