Question

simplify (2-(√5)²+(2+√5)²​

Answer 1

please refer the attached file

Answer 2

ANSWER :-

your answer is

$18 + 8 \sqrt{5}$

EXPLANATION:-

Given :

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

$\tt = (2 + \sqrt{5)} {}^{2} + (2 + \sqrt{5} ) {}^{2}$

$\tiny{= \tt( {2}^{2} + { \sqrt{5} }^{2} + 2 \times 2 \times \sqrt{5} ) + {2 + { \sqrt{5} }^{2} }+ 2 \times 2 \times \sqrt{5}}$

$= \tt(4 + 5 + 4 \sqrt{5} ) + (4 + 5 + 4 \sqrt{5}$

$= \tt(9 + 4 \sqrt{5)} + (9 + 4 \sqrt{5)}$

$= \tt18 + 8 \sqrt{5}$

More to know:-

• (a+b)²= a²+b²+2ab

• (a-b)²= a²+b²-2ab

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