Question

If x is equal to 3 root 5 + 2 root 2 and y is equal to 3 root 5 minus 2 root 2 then evaluate x square - y square​

Answer 1

Step-by-step explanation:

Given-

$x = 3 \sqrt{5} + 2 \sqrt{2 }$

and,

$y = 3 \sqrt{5} - 2 \sqrt{2}$

so,

${x}^{2} = ( {3 \sqrt{5}) }^{2} +2(3 \sqrt{5})(2 \sqrt{2}) + ( {2 \sqrt{2})}^{2}$

$= 45 + 12 \sqrt{10} + 8$

$= 53 + 12 \sqrt{10}$

also,

${y}^{2} = ( {3 \sqrt{5}) }^{2} - 2(3 \sqrt{5})(2 \sqrt{2}) + ( {2 \sqrt{2})}^{2}$

$= 45 - 12 \sqrt{10} + 8$

$= 53 - 12 \sqrt{10}$

Now,

${x}^{2} - {y}^{2} = 24 \sqrt{10}$

Hope it helps!

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