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The difference between squares of two numbers is 120. The square of smallernumber is twice the greater number. Find the numbers.i) |
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Answer» Let the numbers be x and y where x>y so, x^2 - y^2 = 120.....(1) y^2 = 2 x.....(2) Putting (2) in (1), we get x^2 - 2x = 120 x^2 - 2x - 120 = 0 x^2 - 12x + 10x - 120 = 0 x(x -12) +10(x - 12) = 0 (x-12)(x+10) = 0 So x can be 12 or -10, but we are given that the square of smaller number is twice the larger number, therefore the square of any number cant be negative, Thus x cant take value of -10 So x = 12, so y^2 = 2 (12) y^2 = 24 So y = √24 or - √24 y = 2√6 or -2√6 Hence the numbers are 12 and 2√6 or 12 and -2√6 |
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