Question

the difference of squares of 2 numbers is 112. the square of the smaller number is 9 times the larger number. find the numbers

Answer 1

16 and 12

Explanation:

let the 2 numbers be x and y ( x > y ), then

x² - y² = 112 → (1)

y² = 9x → (2)

Substitute y² = 9x into (1)

x² - 9x = 112 ( subtract 112 from both sides )

x² - 9x - 112 = 0 ← in standard form

(x - 16)(x + 7) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 16 = 0 ⇒ x = 16

x + 7 = 0 ⇒ x = - 7

x > 0 , thus x = 16

Substitute x = 16 into (2)

y² = 9(16) = 144 ( take square root of both sides )

y =
`√(144)` = 12

Thus the 2 numbers are 16 and 12

Answer 2

Explanation:

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