2 Answers
1357(x2+14x+9)/(x2+2x+3)=m
(x2+14x+9)=m*(x2+2x+3)
(m-1)x2+(2m-14)x+3m-9=0
x is real implies
D≥0
(2m-14)2-4(m-1)(3m-9)≥0
m2-14m+49-(3m2-12m-+9)≥0
2m2+2m-40≤0
m2+m-20≤0
(m+5)(m-4)≤0
m lies between [-5,4]
1708\hspace{-20}\bf{(62)::\;\;}$ Let $\bf{y=\cos^2 x+\sin^4 x\leq \cos^2 x+\sin^2 x=1}$\\\\\\ So Max. value of $\bf{y=\cos^2 x+\sin^4 x = 1}$\\\\\\ Now for calculation of Minimum....\\\\\\ $\bf{y=1-\sin^2x+\sin^4 x=\left(\sin^2 x-\frac{1}{2}\right)^2+\frac{3}{4}\geq \frac{3}{4}}$\\\\\\ So Min. value of $\bf{y=\cos^2x +\sin^4 x= \frac{3}{4}}$\\\\\\ So range of $\bf{y = f(x)=\cos^2 x=\sin^4 x}$ is $\bf{y\in \left[\frac{3}{4}\;,1\right]}$