Flag Algebra> Sir/Madam, can I please get the answer fo...
question mark

Sir/Madam, can I please get the answer for the following questions:
1.) (x-1)^4+(x-5)^4=82
Solve for x.
2.) (5+2√6)^(x^2-3)+(5-2√6)^(x^2-3)=10
Solve for x.

Pratyasha Panigrahi , 7 Years ago
Grade 12th pass
anser 1 Answers
Arun
Dear student
 
Please only one question in one thread.
 
1.)
 
It's easy to check that x = 4, 2 are two solutions to (x - 1)^4 + (x - 5)^4 = 82. 
Now, we can easily find the other values of x. 
(x - 1)^4 + (x - 5)^4 = 82 
==> (x^4 - 4x^3 + 6x^2 - 4x + 1) + (x^4 - 20x^3 + 150x^2 - 500x + 625) = 82 
==> 2x^4 - 24x^3 + 156x^2 - 504x + 544 = 0 
==> x^4 - 12x^3 + 78x^2 - 252x + 272 = 0. 

By long/synthetic division, 
x^4 - 12x^3 + 78x^2 - 252x + 272 
= (x - 4) (x^3 - 8x^2 + 46x - 68) 
= (x - 4)(x - 2)(x^2 - 6x + 34). 

So, we have 
(x - 4)(x - 2)(x^2 - 6x + 34) = 0 
==> x = 4, 2, or x = 3 ± 5i 
ApprovedApproved
Last Activity: 7 Years ago
star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments