Question

If (15.86 * 15.86 + 15.86 * x + 0.13 * 0.13) is a perfect square, then (100x)² is

Answer 1

Step-by-step explanation:

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Answer 2

Given:

15.86 * 15.86 + 15.86 * x + 0.13 * 0.13 is a perfect square.

To find:

The value of (100x)².

Solution:

As given, we have

$15.86 \times 15.86 + 15.86 \times x + 0.13 \times 0.13$

$= {(15.86)}^{2} + x \times 15.86 \: + {(0.13)}^{2} \: (i)$

which is a perfect square,

Also,

${(a + b)}^{2} = {a}^{2} +2 a b \: + {b}^{2} \: \: (ii)$

So,

On comparing (i) and (ii), we get,

a = 15.86, b = 0.13 and

$2 a b = x \times 15.86$

$2 \times 15.86 \times 0.13 = x \times 15.86$

$x = 2 \times 0.13$

$x = 0.26$

Now,

we need to find (100x)²

So,

On putting the value of x = 0.26 in (100x)², we get,

${(100x)}^{2} = {(100 \times 0.26)}^{2}$

$= {(26)}^{2}$

$= 676$

Hence, (100x)² is equal to 676.