Question 76

What is the sum of the squares of the roots of the equation $$x^2-13x+9=0$$

Solution

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We see that this equation does not have rational roots, 
We will use the identity, 
$$a^2+b^2=\left(a+b\right)^2-2ab$$

We know that the sum of the roots of the equation is 13
And the product of the roots of the equation is 9

So, substituting these values we get, $$13^2-2\left(9\right)=169-18=151$$

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