Question

The difference of squares of two numbers is 45. The square of the smaller number is four times the larger number. Find the numbers.

Answer 1

SOLUTION:-

Given:

•The difference of square of two numbers is 45.

•The square of the smaller number is four times the larger number.

To find:

The numbers.

Explanation:

Assume the larger number be R &

Smaller number be M.

•Smaller number of the square M²=4R

According to the question:

$= > {R}^{2} - {M}^{2} = 45 \\ \\ = > {R}^{2} - 4R = 45 \\ \\ = > {R}^{2} - 4R - 45 = 0 \\ \\ = > {R}^{2} - 9R+ 5R - 45 = 0 \\ \\ = > R(R - 9) + 5(R- 9) = 0 \\ \\ = > (R - 9)(R+ 5) = 0 \\ \\ = > R- 9 = 0 \: \: or \: \:R+ 5 = 0 \\ \\ = >R= 9 \: \: \: or \: \: \: R= - 5$

However, the larger number can't be negative as 4 times of the larger number will be negative & hence, the square of the smaller number will be negative which is not possible.

Therefore,

The larger number is 9.

R= 9

So,

M²= 4R

M²= 4×9

M²= 36

M= √36

M= 6 [smaller Number]

Thus,

The number are 9 & 6.

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