Question

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

I.8^(x+3)+ 8^(-x)=72

II. 5^(y+5)+ 5^(-x)=150

Q: I.8^(x+3)+ 8^(-x)=72 II. 5^(y+5)+ 5^(-x)=150

I. 8^(x+3)+ 8^(-x)=72 8^x × 8^3+ 1/8^x - 72=0 Let 8^x=a 512a+ 1/a- 72=0 512a^2+1-72a=0 512a²-72a+1=0 512a²-64a-8a+1=0 64a (8a-1)-1 (8a-1)= 0 (64a-1)(8a-1)= 0 a= 1/8,1/64 8^x= 1/8 x= -1 8^x= 1/64 x= -2 II.5^(y+5)+ 5^(-y)=150 5^5 × 5^(y )+ 1/5^y -150=0 Let 5^y=b 3125b+ 1/b- 150=0 3125b²-150b+1=0 3125b²-125b-25b+1=0 125b(25b-1)-1(25b-1)= 0 b=1/25,1/125 5^y= 1/25 y= -2 5^y= 1/125 y= -3 Hence, x≥ y