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Question Number 27524 by julli deswal last updated on 08/Jan/18

If x is real, the maximum value of ((3x^2 +9x+17)/(3x^2 +9x+7)) is

Ifxisreal,themaximumvalueof3x2+9x+173x2+9x+7is

Answered by prakash jain last updated on 08/Jan/18

y=((3x^2 +9x+17)/(3x^2 +9x+7)) 3x^2 y+9xy+7y=3x^2 +9x+17 3x^2 (y−1)+9x(y−1)+(7y−17)=0 x∈R⇒Δ≥0 81(y−1)^2 −4×3(y−1)(7y−17)≥0 81(y^2 −2y+1)−12(7y^2 −24y+17)≥0 −3y^2 +126y−123≥0 −y^2 +42y−41≥0 −(y−41)(y−1)≥0 1≤y≤41 min. value of y=1 max. value of y=41

y=3x2+9x+173x2+9x+73x2y+9xy+7y=3x2+9x+173x2(y−1)+9x(y−1)+(7y−17)=0x∈R⇒Δ⩾081(y−1)2−4×3(y−1)(7y−17)⩾081(y2−2y+1)−12(7y2−24y+17)⩾0−3y2+126y−123⩾0−y2+42y−41⩾0−(y−41)(y−1)⩾01⩽y⩽41min.valueofy=1max.valueofy=41

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