Question

x^2-ax-b^2=0.Solve the eqn.

Answer 1

it is a quadratic equation.
we have to solve it to find the value of x.

by using quadratic formula.

Answer 2

x^2−ax−b=(x−a/2)^2−b^2−a^2/4=0x^2−ax−b=(x−a/2)^2−b^2−a^2/4=0

(x−a/2)^2=b^2+a^2/4(x−a^2)^2=b^2+a^2/4

(x−a/2)^2=4b^2+a^2/4(x−a^2)^2=4b^2+a^2/4

(x−a/2) =±(√(4b^2+a^2))/2

Hence x is rational if a/2a/2 is rational and 4b2+a24b2+a2 is the square of a rational number. i.e a right triangle of "short" sides a and 2b has a rational hypotenuse