Question

the difference between the square of two no.is 180.the square of the smaller no. is 8 times the larger no.find the two no. by quadratic formula

Answer 1

Let the two numbers be x and y respectively,

According to the question,

==> Difference of the square of the two numbers = 180

==> x² - y² = 180 { assuming that x > y }

==> x² = 180 + y² ...(1)

Also,

==> The square of the smaller number is 8 times the larger number.

==> y² = 8x ...(2)

Putting y² = 8x in (1)

==> x² = 180 + y²

==> x² = 180 + 8x

==> x² - 8x - 180 = 0

==> x² - 18x + 10x - 180 = 0

==> x(x - 18) + 10(x - 18) = 0

==> (x - 18)(x + 10) = 0

∴ x = 18 , -10

Putting x = 18, -10 in (2)

Case 1: x = 18

==> y² = 8x

==> y² = 8×18

==> y² = 144

==> y = 12, -12

Case 2: x = -10

==> y² = 8x

==> y² = 8×-10

==> y = √-80 { neglected }

Hence, x = 18 , and y = 12 or -12

Answer 2

Answer:

Explanation:

Let the larger number = x

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

and the square of the larger numbe r = x

According to the question,

x - 8x = 180

=> x - 8x - 180 = 0

=> x - 18x + 10x - 180 = 0

=> x(x - 18) + 10(x - 18) = 0

=> (x - 18) (x + 10) = 0

=> x - 18 = 0 or x + 10 = 0

=> x = 18 or x = -10

Thus, the larger number = 18 or -10

Then, the square of the smaller number = 8(18) or 8(-10)

= 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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