Question

If x=5-2√6 then find the value of x²+1/x²


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Answer 1

x=5-2√6

1÷x=1÷(5-2√6)

=(1(5+2√6))÷(5-2√6)(5+2√6)

=(5+2√6)÷(5)^2-(2√6)^2

=(5+2√6)÷25-24

=(5+2√6)÷1

1÷x=5+2√6

x+(1÷x)=(5-2√6)+(5+2√6)

=5-2√6+5+2√6

x+(1÷x)=10

(x+(1÷x))^2=x^2+(1÷x)^2+2(x)(1÷x)

x^2+(1÷x^2)+2=(10)^2

x^2+(1÷x^2)+2=100

x^2+(1÷x^2)=100-2

x^2+(1÷x^2)=98

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