Question

Daca x=radica din 2+radical 3 si y=radical din 6 -1, calculeaza (x la 2 +y la 2-11)la 100

Answer 1

x=√2+√3
x²=(√2+√3 )²=2+3+2√6=5+2√6
y=√6 -1
y²=(√6 -1)²=6+1-2√6=7-2√6
(x² +y²-11)¹⁰⁰=(5+2√6+7-2√6-11)¹⁰⁰=(12-11)¹⁰⁰=1¹⁰⁰=1

Answer 2

$x= \sqrt{2} + \sqrt{3} \\ \\ y= \sqrt{6} -1 \\ \\ (x^2+y^2-11)^{100}=? \\ \\ x^2=( \sqrt{2} + \sqrt{3} )^2= \sqrt{2} ^2+2* \sqrt{2} * \sqrt{3} + \sqrt{3} ^2=2+2 \sqrt{6} +3= \\ =5+ 2\sqrt{6} \\ \\ y^2=( \sqrt{6} -1)^2= \sqrt{6} ^2-2* \sqrt{6} *1+1^2=6-2 \sqrt{6} +1=7-2 \sqrt{6} \\ \\ x^2=5+ 2 \sqrt{6} ~; ~y^2=7-2 \sqrt{6} \\ \\ (x^2+y^2-11)^{100}=(5+2 \sqrt{6} +7-2 \sqrt{6} -11)^1^0^0= (5+7-11)^1^0^0= \\ =(12-11)^1^0^0=1^1^0^0=1$