Divide 16 into two parts in such a way that twice the square of the greater part is 164 more than the square of the smaller part
WBBSE
Class X
Mathematics
Quadratic Equation With One Variable
03 Mark
2025
Let the greater part be x and the smaller part be 16 – x.
The condition is: twice the square of the greater part is 164 more than the square of the smaller part, that is,
2x² = (16 – x)² + 164.
⇒ 2x² = x² – 32x + 256 + 164
⇒ 2x² = x² – 32x + 420
⇒ x² + 32x – 420 = 0
⇒ (x + 42) (x – 10) = 0
x = 10 or x = -42 (rejected)
∴ he two parts are 10 and (16 – 10) = 6
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