Question
Suppose a and b are two roots of the equation x2−(α−4)x+α=0. Find out the maximum possible value of 5ab−a2−b2.
Answer: Option B
:
B
a and b are the roots of the equation
a+b=(α−4),ab=α
5ab−a2−b2
5ab−(a2+b2)
5ab−[(a+b)2−2ab]
5α−[(α−4)2−2α]
5α−[α2−10α+16]
−α2+15α−16=−(α2+15α−16)=−(α2+16α−α−16)=−[α(α+16)−1(α+16)]=−(α+16)(α−1)
So,the maximum value=D4a=[152−4(−1)(−16)]4×1=1614.
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:
B
a and b are the roots of the equation
a+b=(α−4),ab=α
5ab−a2−b2
5ab−(a2+b2)
5ab−[(a+b)2−2ab]
5α−[(α−4)2−2α]
5α−[α2−10α+16]
−α2+15α−16=−(α2+15α−16)=−(α2+16α−α−16)=−[α(α+16)−1(α+16)]=−(α+16)(α−1)
So,the maximum value=D4a=[152−4(−1)(−16)]4×1=1614.
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