Question

Hey, pls answer the 12th question.....

Mark u braniest for step by step explain

Answer 1

Answer:

$(x^{2} +y^{2}+5xy )=39$

Step-by-step explanation:

    $x=\frac{\sqrt{2} -1}{\sqrt{2} +1}$

Now rationalize the denominator.

    $x=\frac{\sqrt{2} -1}{\sqrt{2} +1} *\frac{\sqrt{2} -1}{\sqrt{2} -1} \\\\=>x=\frac{2+1-2\sqrt{2} }{2-1}\\\\ =>x=3-2\sqrt{2}$

Now

     $y=\frac{\sqrt{2} +1}{\sqrt{2} -1} \\\\Rationalize *Denominator\\\\=>y=\frac{\sqrt{2} +1}{\sqrt{2} -1}*\frac{\sqrt{2} +1}{\sqrt{2} +1} \\\\=> y=\frac{2+1+2\sqrt{2} }{2-1} \\\\=>y=3+2\sqrt{2}$

Clue : $(x^{2} +y^{2}+5xy )=(x+y)^2+3xy$

So ,

          $(x^{2} +y^{2}+5xy )\\\\=>(x+y)^2+3xy\\\\=>((3-2\sqrt{2})+(3+2\sqrt{2}) )^2+3(3-2\sqrt{2})(3+2\sqrt{2})\\\\=>6^2+3(9-8)\\\\=>36+3\\\\=>39$

>>> Hope helps you <<<

Answer 2

Rationalisation before solving will reduce the complications in the given question.

#cheers