Question

the difference of the squares of two positive integers is 180. the square of the smaller number is 8 times the larger, find the numbers.​

Answer 1

Answer:

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Answer 2

$\large\underline\mathfrak{\star Question:-}$

☞The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

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$\large\underline\mathfrak\blue{\star Solution:-}$

➢ Let the larger number = x

Then the square of the smaller number = 8 times the larger number = 8x

and the square of the larger number = $x^2$

According to the question,

$\sf{x^2 - 8x = 180}$

$\sf{⟹x^2 - 8x - 180 = 0}$

$\sf{⟹x^2 - 18x + 10x - 180 = 0}$

$\sf{⟹x(x - 18) + 10(x - 18) = 0}$

$\sf{⟹(x - 18) (x + 10) = 0}$

$\sf{⟹x - 18 = 0 or x + 10 = 0}$

$\sf{⟹x = 18 \: or\: x = -10}$

Thus, the larger number = 18 or -10

Then, the square of the smaller number

$\sf{= 8(18) \:or \:8(-10)}$

$\sf{= 144\: or\: -80}$

The square of a number can't be negative, so, the square of smaller number = 144

Hence, the smaller number = $\sqrt{144}$ = 12.

The numbers are 12 and 18.

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