Question: The difference between squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.
Video Explanation
Explanatory Answer
Step 1: Frame equation from information given in the statements
Let the larger number be L.
Let the smaller number be S.
Statement 1: Difference between squares of the two numbers is 180.
i.e., L2 -S2 = 180 ------------(1)
Statement 2: Square of the smaller number is 8 times the larger number.
i.e., S2 = 8L ----------(2)
Substitute S2 = 8L in (1)
L2 - 8L = 180
L2 - 8L - 180 = 0
Step 2: Factorize the quadratic equation to find L
L2 - 18 L + 10 L - 180 = 0
L(L - 18) + 10(L - 18) = 0
(L - 18)(L + 10) = 0
L = 18 and L = -10
If L = 18, S2 = 8 * 18 = 144
S = 12 or - 12
If L = -10, S2 = 8 * (-10) = -80
Square of real number cannot be negative
∴ L = 18 and S = 12; L = 18 and S = -12