Question

In the following questions two equations numbered I and II are given. You have to solve both the equations. Give answer if;

I. 2^(x+2)+ 2^(-x)=5

II. (1/(y+1)+ 1/(y+5))=(1/(y+2)+ 1/(y+4))

Q: I. 2(x+2)+ 2(-x)=5 II. (1/(y+1)+ 1/(y+5))=(1/(y+2)+ 1/(y+4))

2 (x+2) + 2 (-x) =5 2 x ×2² + 1/2 x - 5=0 Put 2 x = a We get 4a+ 1/a- 5=0 4a²+1-5a=0 4a²-4a-a+1=0 (4a-1)(a-1)= 0 a=1,1/4 If 2^x=1 x=0 2^x=1/4 If, 2^x=1/2² x= -2 (1/(y+1)+ 1/(y+5))=(1/(y+2)+ 1/(y+4)) (1/(y+1)- 1/(y+4))=(1/(y+2)- 1/(y+5)) (y+4-y-1)/(y+1)(y+4) = (y+5-y-2)/((y+2)(y+5)) 3/(y+1)(y+4) = 3/((y+2)(y+5)) 1/(y+1)(y+4) - 1/((y+2)(y+5))=0 ((y+2)(y+5)- (y+1)(y+4))/((y+1)(y+4)(y+2)(y+5))=0 y²+7y+10-(y^2+ 5y+4)=0 y²+7y+10-y²-5y-4=0 2y+6=0 y= -3 Hence, x>y