(3+√8)² + 1/(3+√8)²please answer with steps and don't spawn

1.	(3+√8)² + 1/(3+√8)²please answer with steps and don't spawn
Answer» Topic: RATIONALIZATION, Polynomials ________________________________________ To Evaluate $(3+\sqrt{8} )^2+\dfrac{1}{(3+\sqrt{8})^2}$ ________________________________________ Solution What can we observe? We see the TWO terms are all squares. If we try evaluating directly, the calculation will be long, since we should collect like terms. We Can Observe In this SITUATION, we have some algebraic identities to use. Squaring both sides will double the exponent. Here, we are USING $(a+b)^2=a^2+2ab+b^2$ on the sum. Let $t=3+\sqrt{8}$ . Then $\dfrac{1}{t} =3-\sqrt{8}$ . The value of $t+\dfrac{1}{t}$ is so 6. $\rightarrow t+\dfrac{1}{t}=6$ Square both sides. Here, $a=t$ and $b=\dfrac{1}{t}$ . $\rightarrow (t+\dfrac{1}{t})^2=6^2$ $\rightarrow t^2+2\dfrac{t}{t} +\dfrac{1}{t^2} =36$ $\rightarrow t^2+\dfrac{1}{t^2} =34$ After we resubstitute the value of $t$ we get, $\rightarrow (3+\sqrt{8} )^2+\dfrac{1}{(3+\sqrt{8} )^2} =34$ So, the value of evaluation is 34.

Answer»

Topic: RATIONALIZATION, Polynomials

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To Evaluate

$(3+\sqrt{8} )^2+\dfrac{1}{(3+\sqrt{8})^2}$

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Solution

What can we observe?

We see the TWO terms are all squares. If we try evaluating directly, the calculation will be long, since we should collect like terms.

We Can Observe

In this SITUATION, we have some algebraic identities to use. Squaring both sides will double the exponent. Here, we are USING $(a+b)^2=a^2+2ab+b^2$ on the sum.