Divide 20 into two parts such that twice the square of the smaller part is 16 less than the square of the larger part. Solve it as a quadratic equation. Ans.=12, 8 as given in textbook.
Answers
Answer:
Step-by-step explanation:
Let the smaller part be x
Larger part be (20-x)
A/Q
2x²+16=(20-x)²
From this equation we get
X=-48,x=8,
Where x>0,
Hence x=8,and the numbers are
8 and
(20-x) =12
Answer: -48, 8
Explanation:
Let the smaller part be x
Hence the larger part is (20 – x)
(Since x + (20 - x) = 20)
Square of the smaller part is given by x^2
Twice the square of the smaller part is given by 2(x^2)
Therefore, 2(x^2) + 16 = (20 – x)^2
2(x^2) + 16 = (400 – 40x + x^2)
2(x^2) - x^2 + 40x - 400 + 16 = 0
x^2 + 40x - 384 = 0
x^2 + 48x - 8x - 384 = 0
x(x + 48) -8(x + 48) = 0
(x + 48) ( x - 8) = 0
x = -48, x = 8
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