If a and b are the roots of the equation, $x^{2}$ – 6x + 1 = 0, then the value of $a^{2}$ + $b^{2}$ is __

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Solution

Step 1:- For, $x^{2}$ – 6x + 1 = 0, sum of roots = 6= a+b and product of roots = ab =1

Step 2:- $a^{2}$ + $b^{2}$ = $(a + b)^{2}$ – 2ab

Step 3:- $a^{2}$ + $b^{2}$ = $6^{2}$ – 2(1) = 36 - 2 =34

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