Solve (5 + sqrt(5)) ^ - 19 * 31x * (- sqrt(5) + sqrt(5)) | Equatix - Math Solver

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3(r+2s)=2t-4

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3(r+2s)=2t-4

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Question

$$(5+\sqrt{5})^{-19}{31x}(-\sqrt{5}+\sqrt{5})$$

Evaluate

$0$

Solution Steps

Use the distributive property to multiply $\left(5+\sqrt{5}\right)^{-19}\times 31x$ by $-\sqrt{5}+\sqrt{5}$.

$$31\left(5+\sqrt{5}\right)^{-19}x\left(-\sqrt{5}\right)+31\left(5+\sqrt{5}\right)^{-19}x\sqrt{5}$$

Multiply $31$ and $-1$ to get $-31$.

$$-31\left(5+\sqrt{5}\right)^{-19}x\sqrt{5}+31\left(5+\sqrt{5}\right)^{-19}x\sqrt{5}$$

Combine $-31\left(5+\sqrt{5}\right)^{-19}x\sqrt{5}$ and $31\left(5+\sqrt{5}\right)^{-19}x\sqrt{5}$ to get $0$.

$$0$$

Factor

$0$