Question

if x=3+√5/3-√5 and y=3-√5/3+√5 then evaluate x^2-xy+y^2
can someone please answer this question?? asap??!!

Answer 1

X=(3+ root 5)/(3-root5)
X=( 3+root 5)²/(3²-5)=(14+6root5)/4
Y=(3-root5)/(3+root5)=(3-root5)²/(3²-5)
Y=(14-6root5)/4
So.. x² - xy + y²
=(14+root5)²/16 - (14²- 180)/16 + (14 - root5)²/16
=1/16 ×[ (14+root5) ² + (14- root5) ² -( 196 - 180)]
=1/16× [2(14² + (root5) ²) - 16]
= 1/16×[2(196 + 5) - 16] = 1/16×[ 402 - 16]
= 386/16 = 193/8.. Ans.
Hope this is ur required answer.