यदि `x=(1)/(2-sqrt(3))` हो, तो `x^(3)-2x^(2)-7x+5` का मान ज्ञात करो।

Explanation

दिया है की
`x=(1)/(2-sqrt(3))=(1)/(2-sqrt(3))xx(2+sqrt(3))/(2+sqrt(3))=(2+sqrt(3))/(2^(2)-(sqrt(3))^(2))=(2+sqrt(3))/(4-3)=2+sqrt(3)`
`rArr x-2=sqrt(3)`
`rArr (x-2)^(2)=(sqrt(3))^(2)`
`rArr x^(2)-4x+4=3 rArr x^(2)-4x+1=0" "...(i)`
` :. x^(3)-2x^(2)-7x+5=x(x^(2)-4x+1)+2(x^(2)-4x+1)+3`
`= x xx 0+2xx0+3=0 " " [ :. x^(2)-4x+1=0]`