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If (10.24 × 10.24) - (10.24 × A) + (0.24 × 0.24) is a perfect square, then find the value of 'A'.
Question

If (10.24 × 10.24) - (10.24 × A) + (0.24 × 0.24) is a perfect square, then find the value of 'A'.

A.

0.24

B.

0.36

C.

0.48

D.

0.12

Correct option is C

As we know,
(a - b)2^2​ = a2^2​+ b2^2​ - 2ab
=>(10.24 × 10.24)- (10.24 x A) + (0.24 × 0.24)
=> (10.24)2^2​ – (10.24 × A) + (0.24)2^2​​
(10.24 – 0.24)2^2​ = 10.242^2​ + 0.242^2​ – 2 × 10.24 × 0.24
On comparing,
=>2 × 10.24 × 0.24=10.24 × A
A = 0.48
As we can see from Venn diagram only 1 condition is true .

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