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Let a^(2)+b^(2)=a^(2)+beta^(2)=2. Then s...

Let `a^(2)+b^(2)=a^(2)+beta^(2)=2`. Then show that the maximum value of `S=(1-alpha)(a-b)+(1-alpha)(1-beta)` is 8.

Text Solution

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Let `alpha=sqrt(2)cos theta, b=sqrt(2)sin theta`.
`alpha=sqrt(2)cos phi, beta=sqrt(2)sin phi`
`rArr S=2-2(sin(theta+pi//4))+sin(phi+pi//4)+2[cos(theta-phi)]`
Maximum value occurs when `theta=phi=5pi//4`
`rArr S_("max")=2[-1-1]+2=8`
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