Question

if 3.9 power x = 27y and 64 power x = 256y then find x and y​

Answer 1

Answer:

x+y=4x+y=4 and xx+yy=64xx+yy=64. What are xx and yy?

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Gopal Menon, B Sc (Hons) Mathematics, Indira Gandhi National Open University (2010)

Updated October 2, 2017 · Upvoted by Bihan Sen, M.Tech Computer Science & Mathematics, Indian Statistical Institute, Kolkata (2019) and Parth Trivedi, M.Sc. Mathematics, Bhavnagar University (2008)

Originally Answered: If x+y=4 and x^x+y^y=64. Find x and y ?

We want to determine the values of xx and yy given that x+y=4x+y=4 and xx+yy=64.xx+yy=64.

This problem cannot be solved analytically. However, it can be solved numerically as under, using the Newton Raphson method.

y=4−xy=4−x

⇒xx+(4−x)(4−x)=64.⇒xx+(4−x)(4−x)=64.

Let z=xx+(4−x)(4−x)−64.z=xx+(4−x)(4−x)−64.

⇒dzdx=xx(1+logx)−(4−x)(4−x)(1+log(4−x)).⇒dzdx=xx(1+log⁡x)−(4−x)(4−x)(1+log⁡(4−x)).

Answer 2

Answer:

Given,

3.9x=27y

64x=256y

then,

x=4 & y=3