The sum of all the roots of the equation |x^2 | vedclass

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(A) The given equation is $|x^2-8x+15|-2x+7=0$.Case $1$: $x^2-8x+15 \geq 0$,which implies $x \leq 3$ or $x \geq 5$.The equation becomes $x^2-8x+15-2x+

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$9+\sqrt{3}$

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(A) The given equation is $|x^2-8x+15|-2x+7=0$.Case $1$: $x^2-8x+15 \geq 0$,which implies $x \leq 3$ or $x \geq 5$.The equation becomes $x^2-8x+15-2x+7=0$,so $x^2-10x+22=0$.The roots are $x = \frac{10 \pm \sqrt{100-88}}{2} = 5 \pm \sqrt{3}$.Since $5+\sqrt{3} \geq 5$ and $5-\sqrt{3} \approx 3.268$ (which is not $\leq 3$ or $\geq 5$),only $x = 5+\sqrt{3}$ is a valid root.Case $2$: $x^2-8x+15 The equation becomes $-(x^2-8x+15)-2x+7=0$,so $-x^2+8x-15-2x+7=0$,which simplifies to $-x^2+6x-8=0$ or $x^2-6x+8=0$.Factoring gives $(x-2)(x-4)=0$,so $x=2$ or $x=4$.Since $3 The sum of all roots is $(5+\sqrt{3}) + 4 = 9+\sqrt{3}$.

The sum of all the roots of the equation $|x^2-8x+15|-2x+7=0$ is:

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