Question

Simplify ( 2 √2 - 5 )² + (3 √2 +3)² - (√2 - 1 )² . Thanks for solving . Stay Safe

Answer 1

Step-by-step explanation:

(2√2-5)²=33-20√2 by( a-b)²=a²-2ab+b²

(3√2+√3)²=21+6√6 by (a+b)²=a²+2ab+b²

(√2-1)²=3-2√2 by (a-b)²=a²-2ab+b²

=(33-20√2)+(21+6√6)-(3-2√2)

=33-20√2+21+6√6-3+2√2

=51-18√2+6√6

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Answer 2

Answer:

By using ALGEBRAIC IDENTITIES

(a+b)²=a²+b²+2ab

(a-b)²=a²+b²-2ab

$= {(\sqrt[2]{2} - 5) }^{2} + {( \sqrt[3]{3} + 3) }^{2} - </em><em>\</em><em>\</em><em>{( \sqrt{2} - 1)}^{2}$

$= {( \sqrt[2]{2}) }^{2} + {(5)}^{2} - 2( \sqrt[2]{2} )(5) + </em><em>\</em><em>\</em><em> {( \sqrt[3]{2} )}^{2} + {(3)}^{2} + 2( \sqrt[3]{2} )(3) - </em><em>\</em><em>\</em><em>( { \sqrt{2} })^{2} + {(1)}^{2} - 2(1)( \sqrt{2} )$

$= 8 + 25 - \sqrt[20]{2} + 18 + 9 + </em><em>\</em><em>\</em><em>\sqrt[18]{2} - 2 + 1 - \sqrt[2]{2}$

$= 59 - \sqrt[20]{2} + \sqrt[20]{2}$

$= 59$

The required ANSWER is 59

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