If x to the power 4 plus 1 upon x to the power 4 equals 47 then what will be x to the power 3 plus 1 upon x to the power 3 equals what?

Answer 1

A similar question can be solved as below : If x to the power 4 plus 1 upon x to the power 4 equals 23 then what will be (x minus 1 upon x) to the power 2 equals what?

a2 + b2 = (a + b)^2 - 2ab.

so (x^2 )^2 + (1/x2)^2 = (x^2 + 1/x^2)^2 - 2 = 23.

so (x^2 + 1/x^2) = 5.

therefore

(x - 1/x)^2 = (x^2 + 1/x^2) -2 = 5 -2 = 3.