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.​

Answer 1

$\huge\blue{ANSWER:-}$

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Let the larger number be x.

Square of larger number = x

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

ATQ,

• x2-8x 180

• x-8x- 180 0

By factorisation,

➭x2-18x+ 10x 180 =0

➭x(x-18)+10 (x - 18) = 0

➭x-18) (x +10) = 0

➭x 18 0 or x+10 O

➭x=-10

➭x= 18 or Taking x = 18 we get,

➭Larger number = x = 18

➟smaller numBer = V(8x) = V(8x18) =v144 = 12

➼Takingx =-10

➼Larger number = -10

∴Smaller number. = V(8x) = V(8x-10) = V-80

Not possible.

∴The two numbers are 18 and 12.

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