Question

Find all real solutions to the following equation 4x^2+x√2-1-0

Answer 1

The Equation

4x^2 + x√2 - 1  =  0

Compare it to quadratic form ax^2 + bx + c  =  0

a = 4, b = √2, c = -1

Roots are  

x  =  [ - b ± √(b^2 - 4ac) ] / 2a

x  =  { - √2 ± √[ (√2)^2 - 4(4)(-1) ] } / 2(4)

x  =  [ - √2 ± √(2 + 16) ] / 8

x  =  [ - √2 ± √[18 ] / 8

x  =  [ - √2 ± 3√2 ] / 8

x  =  [ - √2 + 3√2 ] / 8       ;        x  =   [ - √2 - 3√2 ] / 8

x  =  [ 2√2 ] / 8       ;        x  =   [ - 4√2 ] / 8

x  =  √2 / 4       ;        x  =   - √2 ] / 2

Answer :

The Solutions are x  =  √2 / 4 and x  =   - √2 ] / 2.