If x is real, then the maximum and minimum values of the expression x2−3x+4x2+3x+4  will be

Lety=x2−3x+4x2+3x+4 ⇒(y−1)x2+3(y+1)x+4(y−1)=0For x is real D≥0 ⇒9(y+1)2−16(y−1)2≥0 ⇒−7y2+50y−7≥0⇒7y2−50y+7≤0 ⇒(y−7)(7y−1)≤0Now, the product of two factors is negative if one in -ve and one in +ve .Case I : (y−7)≥0 and (7y−1)≤0            ⇒y≥7 and y≤17 But it is impossibleCase II : (y−7)≤0 and (7y−1)≥0             ⇒y≤7 and y≥17⇒17≤y≤7           Hence maximum value is 7 and minimum value is 17