Solve (sqrt{5}-2)^2+4(sqrt{5}-2)=1

$$( \sqrt { 5 } - 2 ) ^ { 2 } + 4 ( \sqrt { 5 } - 2 ) = 1$$

Verify

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\sqrt{5}-2\right)^{2}.

$$\left(\sqrt{5}\right)^{2}-4\sqrt{5}+4+4\left(\sqrt{5}-2\right)=1$$

The square of \sqrt{5} is 5.

$$5-4\sqrt{5}+4+4\left(\sqrt{5}-2\right)=1$$

Add 5 and 4 to get 9.

$$9-4\sqrt{5}+4\left(\sqrt{5}-2\right)=1$$

Use the distributive property to multiply 4 by \sqrt{5}-2.

$$9-4\sqrt{5}+4\sqrt{5}-8=1$$

Combine -4\sqrt{5} and 4\sqrt{5} to get 0.

$$9-8=1$$

Subtract 8 from 9 to get 1.

$$1=1$$

Compare 1 and 1.

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