what is an equation whose root are 5 + √2 and 5 – √2?a. x² – 10x + 23 = 0b. x² + 10x + 23 = 0c. x² + 10x – 23 = 0d. x10 – 10x – 24 = 0. Created by paulacristina. Math

what is an equation whose root are 5 + √2 and 5 – √2?a. x²

Hanimeya

Verified answer

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PROBLEM :

what is an equation whose root are 5 + √2 and 5 – √2?

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ANSWER :

$\purple{ \bold{a. \: x² – 10x + 23 = 0}}$

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FORMULA :

$\bold{ \frac{ - b ± \sqrt{ {b}^{2} } - 4ac }{2a} }$

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SOLUTION :

This kind of quadratic equation gives two solutions, one when ± is addition and one when it is subtraction, now let's solve to get those two solution.

$\small\begin{array}{|c|}\hline \\ \: \: \: \tiny x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\times 23}}{2} \: \: \: \\ \tiny x=\frac{-\left(-10\right)±\sqrt{100-4\times 23}}{2} \: \: \: \: \: \: \: \: \\ \tiny \: x=\frac{-\left(-10\right)±\sqrt{8}}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tiny x=\frac{-\left(-10\right)±2\sqrt{2}}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tiny \: x=\frac{10±2\sqrt{2}}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tiny \: x=\frac{2\sqrt{2}+10}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tiny x=\sqrt{2}+5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tiny \: x=\frac{10-2\sqrt{2}}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \tiny \: x=5-\sqrt{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: \\ \hline \end{array} \\ \\ \\ \\ \tt \: the \: equation \: is \: now \: solved : \\ \\ \: \: \: \boxed{ \purple{ \bold {x= +5 \sqrt{2} \: : \: x=5-\sqrt{2} }} }$