x+1/x=17/4 sqaure completion method
jhj:
can no body solve this
i am still alive and any maths question can't stop my brain from solving it.
ok then sole4
i had solved it.
Answers
Answered by
1
X+1/x=17/4
x²+1=17/4X
x²-17/4x=-1
now,
Third term=(1/2 coefficent of x)²
=1/4*289/16)
so...adding thid term in above equation,
x²-17/4x+289/64=289/64 -1
(x-17/8)²=225/64
taking squareroot
x-17/8=15/8 or x-17/8=-15/8
ans...
x=4 or x=1/4
x²+1=17/4X
x²-17/4x=-1
now,
Third term=(1/2 coefficent of x)²
=1/4*289/16)
so...adding thid term in above equation,
x²-17/4x+289/64=289/64 -1
(x-17/8)²=225/64
taking squareroot
x-17/8=15/8 or x-17/8=-15/8
ans...
x=4 or x=1/4
Answered by
1
x+1/x=17/4
x^2+1/x=17/4
4(x^2+1)=17x
4x^2+4=17x
4x^2-17x+4=0
4x^2-16x-x+4=0
4x(x-4)-1(x-4)=0
(4x-1)(x-4)=0
4x-1=0 x-4=0
4x=1 x=4
x=1/4
Therefore, x=4 or 1/4
x^2+1/x=17/4
4(x^2+1)=17x
4x^2+4=17x
4x^2-17x+4=0
4x^2-16x-x+4=0
4x(x-4)-1(x-4)=0
(4x-1)(x-4)=0
4x-1=0 x-4=0
4x=1 x=4
x=1/4
Therefore, x=4 or 1/4
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