Apply the appropriate property to simplify the follow expression:
Answers
If x^2+1/x^2=27, what is the value of 3x^3+5x-3/x^3-5/x?
Answer
4
Follow
Request
More
Ad by Amazon India
Lowest price ever.
Get OnePlus 6T at the lowest price ever during the Amazon Fab Phones Fest.
Learn More
2 ANSWERS

Vandana Kapoor, M.Sc.,B.Ed. Mathematics & Science, Hemvati Nandan Bahuguna Garhwal University, Uttarakhand, India (2003)
Answered May 5, 2018
We know that(a-b)^2=a^2+b^2–2ab
Putting a=x,b=1/x
(x-1/x)^2=x^2+1/x^2–2×x×1/x
=x^2+1/x^2–2
=27–2=25
(x-1/x)^2=25
Taking squareroot of both sides
x-1/x=5
Now(3x^3–3/x^3)+(5x-5/x)
=3(x^3–1/x^3)+5(x-1/x)
=3(x-1/x)(x^2+1/x^2+1)+5×5
=3×5×(27+1)+25
=15×28+25
=420+25=445
459 Views · View Upvoters · Answer requested by Ansh Jaiswal
Upvote· 3
Share

Comment...
RecommendedAll

Susai Raj, former Retired Teacher.
Answered May 5, 2018
x^2 + 1/x^2 = 27
(x - 1/x)^2 = x^2 + 1/x^2 - 2×x×1/x
ie. (x - 1/x)^2 = 27 - 2 = 25
So. (x - 1/x) = 5
(x - 1/x)^3 = x^3 - 1/x^3 - 3×x×1/x(x - 1/x)
5^3 = x^3 - 1/x^3 - 3×5
125 = x^3 - 1/x^3 - 15
x^3 - 1/x^3 = 125 + 15
x^3 - 1/x^3 = 140 . So
3x^3 + 5x - 3/x^3 - 5/x
= 3(x^3 - 1/x^3) +5(x - 1/x)
= 3 × 140 + 5×5
=420 + 25 = 445