Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.

$x^{2} - (\sqrt{2} + 1) x + \sqrt{2} = 0$

Open in App

Solution

The given equation is
$x squared minus left parenthesis square root of 2 plus 1 right parenthesis x plus square root of 2 equals 0 rightwards double arrow x squared minus 2 cross times left parenthesis fraction numerator square root of 2 plus 1 over denominator 2 end fraction right parenthesis x plus left parenthesis fraction numerator square root of 2 plus 1 over denominator 2 end fraction right parenthesis squared minus left parenthesis fraction numerator square root of 2 plus 1 over denominator 2 end fraction right parenthesis squared plus square root of 2 equals 0 rightwards double arrow left parenthesis x minus fraction numerator square root of 2 plus 1 over denominator 2 end fraction right parenthesis squared equals left parenthesis fraction numerator square root of 2 plus 1 over denominator 2 end fraction right parenthesis squared minus square root of 2 equals fraction numerator 2 plus 1 plus 2 square root of 2 over denominator 4 end fraction minus square root of 2 equals fraction numerator 1 minus 2 square root of 2 plus 2 over denominator 4 end fraction rightwards double arrow left parenthesis x minus fraction numerator square root of 2 plus 1 over denominator 2 end fraction right parenthesis squared equals left parenthesis fraction numerator 1 minus square root of 2 over denominator 2 end fraction right parenthesis squared rightwards double arrow left parenthesis x minus fraction numerator square root of 2 plus 1 over denominator 2 end fraction right parenthesis equals plus-or-minus left parenthesis fraction numerator 1 minus square root of 2 over denominator 2 end fraction right parenthesis rightwards double arrow x equals fraction numerator square root of 2 plus 1 over denominator 2 end fraction plus-or-minus left parenthesis fraction numerator 1 minus square root of 2 over denominator 2 end fraction right parenthesis rightwards double arrow x equals 1 space o r space square root of 2$

Suggest Corrections

Similar questions

Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.
$2 x^{2} + x + 4 = 0$

Fint the roots of the following quadratic equations (if they exist) by the method of completing the square.
$3 x^{2} + 11 x + 10 = 0$

x^{2} - (\sqrt{2} + 1) x + \sqrt{2} = 0

x^{2} - (\sqrt{2} + 1) x + \sqrt{2} = 0

Join BYJU'S Learning Program