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The difference of squares of two numbers is 180. The square of smaller number is 8 timesthe larger number. Find the two numbers.23. |
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Answer» Let the larger number = xThen the square of thesmaller number= 8 times the larger number = 8xand the square of thelarger number = x²According to the question, x² - 8x = 180 => x²- 8x - 180 = 0 => x²- 18x + 10x - 180 = 0 => x(x - 18) + 10(x - 18) = 0 => (x - 18) (x + 10) = 0 => x - 18 = 0orx + 10 = 0 => x = 18orx = -10 Thus, the larger number = 18 or -10Then, the square of the smaller number= 8(18)or 8(-10)= 144 or -80 The square of a number can't benegative, so, thesquare of smaller number =144Hence, thesmaller number =√(144) =12The numbers are12and18 thank you |
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