Mathematics
Divide 20 into two parts such that the sum of their squares is 272. The larger of two parts is square of the other. Assuming the smaller part to be ‘x’, form an equation and solve it to find the two parts.
Quadratic Equations
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Answer
Let two parts be x and (20 - x).
Given,
Sum of squares = 272
⇒ x2 + (20 - x)2 = 272
⇒ x2 + (400 - 2 × 20 × x + x2) = 272
⇒ x2 + (400 - 40x + x2) = 272
⇒ 2x2 - 40x + 400 = 272
⇒ 2x2 - 40x + 400 - 272 = 0
⇒ 2x2 - 40x + 128 = 0
⇒ 2(x2 - 20x + 64) = 0
⇒ x2 - 20x + 64 = 0
⇒ x2 - 16x - 4x + 64 = 0
⇒ x(x - 16) - 4(x - 16) = 0
⇒ (x - 4) = 0 or (x - 16) = 0 [Using zero product rule]
⇒ x = 4 or x = 16.
Hence, the two parts are 4 and 16.
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