If f2(x)+2g2(x)+3h2(x)≤1 and u(x)=2f(x)−2g(x)+3h(x), then the maximum value of u2(x) is equal to
A
9.0
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B
9.00
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C
9
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Solution
Let two vectors →P=f(x)^i+√2g(x)^j+√3h(x)^k and →Q=2^i−√2^j+√3^k
if θ is the angle between →P and →Q,
then cosθ=→P⋅→Q|→P||→Q|=2f(x)−2g(x)+3h(x)√f2(x)+2g2(x)+3h2(x)×√4+2+3⇒[2f(x)−2g(x)+3h(x)]2(f2(x)+2g2(x)+3h2(x))×9≤1[∵cos2θ≤1]⇒u2(x)≤9(f2(x)+2g2(x)+3h2(x))⇒u2(x)≤9×1⇒u2(x)≤9