Question

X− 3 = 1 /x find the value of x2 + 1 /x2?

Answer 1

Answer:

Step-by-step explanation:

As per the question, we have

x+1x=11

∴(x+1x)2=(11)2 ... [Squaring both sides]

∴x2+1x2+2(x)(1x)=121

∴x2+1x2+2(x

)(1x

)=121

∴x2+1x2+2=121

∴x2+1x2=121−2=119 ... (i)

Now, back to x+1x=11

(x+1x)4=(11)4

∴x4+1x4+4(x3)(1x)+6(x2)(1x2)+4(x)(1x3)=(11)4

∴x4+1x4+4(x2)+6+4(1x2)=14641

∴x4+1x4+4(x2)+4(1x2)=14641−6

∴x4+1x4+4(x2+1x2)=14635

∴x4+1x4+4(119)=14635 ... [Substituting the value of x2+1x2 from (i)]

∴x4+1x4+476=14635

∴x4+1x4=14635−476

∴x4+1x4=14159

Hence, the answer.