How do you simplify (sqrt(7) + sqrt(5))^4 + (sqrt(7) - sqrt(5))^4?

1 Answer
Feb 7, 2015

Okay i should thank you for such a question

OK lets start

Call sqrt 7 =sqrta and sqrt 5 =sqrtb

So lets rewrite you equation as {( sqrta + sqrtb) ^2}^2 +{ ( sqrta -sqrt b )^2 }^2

So lets take the first part and simplify

( sqrta + sqrtb) ^2 = a + 2 sqrt(ab) + b

So lets substitute 7 + 5 + 2 sqrt35 = 12 + sqrt 35

Square this gain and you will get that {( sqrta + sqrtb) ^2}^2 =144 + 35 + 24 sqrt(35)= 179+ 24sqrt 35

Similarly repeat the above steps for { ( sqrta -sqrt b )^2 }^2

After substituting you should get that the above equation is = 179 - 24sqrt35

So finally lets put the puzzle together

hence {( sqrta + sqrtb) ^2}^2 +{ ( sqrta -sqrt b )^2 }^2= 179 + 24 sqrt35 + 179 - 24sqrt35

(sqrt(7) + sqrt(5))^4 + (sqrt(7) - sqrt(5))^4 = 358

Hope that this is what you wanted if this is what you wanted please write down in the comments