If a - b -5 and a - b -3- then the value of a 2- b 2 is equal to 4 -A- TrueB- False

The correct option is A True We know that a^2+b^2=1/2× 2 (a^2+b^2) =1/2{(a+b)^2+(a b)^2} (by formula) =1/2{(√(5))^2+(√(3))^2}=1/2(5+3) =1/2× 8=4 So, the statem ...

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Byju's Answer

Standard X

Mathematics

Composition of Function

If a + b =√5 ...

Question

If $a + b = \sqrt{5}$ and $a - b = \sqrt{3}$ , then the value of $a^{2} + b^{2}$ is equal to 4.

True

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False

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Solution

The correct option is A
True

We know that $a^{2} + b^{2} = \frac{1}{2} \times 2 (a^{2} + b^{2})$

$= \frac{1}{2} {(a + b)^{2} + (a - b)^{2}}$ (by formula)

$= \frac{1}{2} {(\sqrt{5})^{2} + (\sqrt{3})^{2}} = \frac{1}{2} (5 + 3)$

$= \frac{1}{2} \times 8 = 4$

So, the statement is true.

Suggest Corrections

Similar questions

Q. Simplify

\frac{5}{a + b} - \frac{4}{a - b} + \frac{8 a}{a^{2} - b^{2}}

, then the answer is

\frac{9}{a + b}

If true then enter

1

and if false then enter

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For two square matrices A and B of the same order, $(A + B) (A - B)$ = $A^{2} - B^{2}$ .

Q. If

*

is defined by

a * b = a - b^{2}

and

\oplus

is defined by

a \oplus b = a^{2} + b

, where

a

and

b

are integers, then

(3 \oplus 4) * 5

is equal to

Q. State whether the statement is True or False.

(\frac{a}{2} - \frac{b}{3}) (\frac{a}{2} + \frac{b}{3})

is equal to

\frac{a^{2}}{4} - \frac{b^{2}}{9}

Q. If

a + b = 8, a - b = 4

, then

a^{2} + b^{2}

is equal to:

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If a+b=√5 and a−b=√3, then the value of a2+b2 is equal to 4.

The correct option is A True We know that a2+b2=12×2(a2+b2) =12{(a+b)2+(a−b)2} (by formula) =12{(√5)2+(√3)2}=12(5+3) =12×8=4 So, the statement is true.

If $a + b = \sqrt{5}$ and $a - b = \sqrt{3}$ , then the value of $a^{2} + b^{2}$ is equal to 4.

The correct option is A
True

We know that $a^{2} + b^{2} = \frac{1}{2} \times 2 (a^{2} + b^{2})$

$= \frac{1}{2} {(a + b)^{2} + (a - b)^{2}}$ (by formula)

$= \frac{1}{2} {(\sqrt{5})^{2} + (\sqrt{3})^{2}} = \frac{1}{2} (5 + 3)$

$= \frac{1}{2} \times 8 = 4$

So, the statement is true.