Let `P(x)=5/4+6x-9x^2a n dQ(y)=-4y^2+4y+(13)/2dot` if there exists unique pair of real numbers `(x , y)` such that `P(x)Q(y)=20` , then the value of `(6x+10 y)` is _____.

Answer

3

Explanation

We have `P(x)=(5)/(3)-6 x-9x^(2)=-(3x+1)^(2)=-(3x+1)^(2)+(8)/(3)`
`impliesP_("max")=(8)/(3)`
Similarly, `Q(y)=-4y^(2)+4y+(13)/(2)=-(2y-1)^(2)+(15)/(2)`
`Q_(max)=(15)/(2)`
Now, `P_(max)xxQ_("max)=(8)/(3)xx(15)/(2)=20`
So, `(x,y)-=(-(1)/(3),(1)/(2))`
Hence, `6x+10y=6((-1)/(3))+10((1)/(2))=-2+5=3`