Match the following Columns

Question

Professor PC Thomas Classes · Answer

(A) Put $y=\frac{6-x+8-x}{2}=7-x$. Equation reduces to $y^{4}+6y^{2}-7=0 \Rightarrow y^{2}=1 \Rightarrow y=\pm 1 \Rightarrow x=8, 6$. (B) $y=x-3 \Rightarrow (y+1)^{6}+(y-1)^{6}=64 \Rightarrow 2(y^{6}+15y^{4}+15y^{2}+1)=64 \Rightarrow y^{2}=1 \Rightarrow x=4, 2$. (C) $x^{2}+x=t \Rightarrow t(t-2)=24 \Rightarrow t^{2}-2t-24=0 \Rightarrow t=6, -4 \Rightarrow x=2$ etc. (D) Put $\frac{x^{2}+x+1}{x-1}=t$, proceed to get $x=6$.