Question

if x+1/x=5/2 find the value of (i) x-1/x (ii) x^3 + 1/x^3

Answer 1

Answer:

Given, x−x1=5

Given, x−x1=5Squaring both the sides,

Given, x−x1=5Squaring both the sides,⇒(x−x1)2=52

Given, x−x1=5Squaring both the sides,⇒(x−x1)2=52⇒x2+x21−2(x)(x1)=25

Given, x−x1=5Squaring both the sides,⇒(x−x1)2=52⇒x2+x21−2(x)(x1)=25⇒x2+x21=25+2

Given, x−x1=5Squaring both the sides,⇒(x−x1)2=52⇒x2+x21−2(x)(x1)=25⇒x2+x21=25+2⇒x2+x21=27

Given, x−x1=5Squaring both the sides,⇒(x−x1)2=52⇒x2+x21−2(x)(x1)=25⇒x2+x21=25+2⇒x2+x21=27Now,

Given, x−x1=5Squaring both the sides,⇒(x−x1)2=52⇒x2+x21−2(x)(x1)=25⇒x2+x21=25+2⇒x2+x21=27Now,x3−x31

Given, x−x1=5Squaring both the sides,⇒(x−x1)2=52⇒x2+x21−2(x)(x1)=25⇒x2+x21=25+2⇒x2+x21=27Now,x3−x31=(x−x1)[(x)2+(x1)2+(x)(x1)]

Given, x−x1=5Squaring both the sides,⇒(x−x1)2=52⇒x2+x21−2(x)(x1)=25⇒x2+x21=25+2⇒x2+x21=27Now,x3−x31=(x−x1)[(x)2+(x1)2+(x)(x1)]=5(27+1)

Given, x−x1=5Squaring both the sides,⇒(x−x1)2=52⇒x2+x21−2(x)(x1)=25⇒x2+x21=25+2⇒x2+x21=27Now,x3−x31=(x−x1)[(x)2+(x1)2+(x)(x1)]=5(27+1)=140