Question

Prove without using calculator,
[5^(1/2)+2]^4+[5^(1/2)-2]^4=322

someone pls help me....

Answer 1

at all amounts to reading the notation correctly and applying it

Answer 2

i dont see any "easy" way around it other than its given to you to prcatice seeing how the math is done

Answer 3

expand it all out and add it all together;

what part are you stuck with?

Answer 4

without using calculator...

Answer 5

we could prolly clean it up a bit using abstract notations; but in the end the math still has to be done

Answer 6

use \[(a+b)^4=a^4+4a^3b+4a^2b^2+4ab^3+b^4\]??

Answer 7

that should be a\[6a^2b^2\]

Answer 8

(A+n)^4 + (A-n)^4 = 322

(A^2+ 2An +n^2)^2 + (A^2 - 2An +n^2)^2

A^2+ 2An +n^2
A^2+ 2An +n^2
--------------
A^4 +A^3(2n) + (An)^2
+A^3(2n) +4(An)^2 +2A n^3
+ (An)^2 +2A n^3 + n^4
------------------------------------
A^4 + 2nA^3 + 6(An)^2 + 4A n^3 + n^4

yeah, binomial expansion might be quicker

Answer 9

ok... maybe i calculate wrongly...

Answer 10

One thing about conjugates if that if
\[(a+b\sqrt{c})^n = x+y\sqrt{c}\]
then:
\[(a-b\sqrt{c})^n = x-y\sqrt{c}\]

Answer 11

and since the next one has -n we simply switch odds powers

A^4 + 4A^3 n + 6(An)^2 + 4A n^3 + n^4
A^4 - 4A^3 n + 6(An)^2 - 4A n^3 + n^4
------------------------------------
2A^4 +12(An)^2 +2n^4

Answer 12

ok i get it...
is \[(a+b)^4=a^4+4a^3b+4a^2b^2+4ab^3+b^4\]

Answer 13

2(sqrt(5))^4 + 12(2sqrt(5))^2 +2(2)^4 = 322 ??

Answer 14

2(5.5) + 12(4.5) + 2(4.4)

50 + 240 + 32 = 322 ??


1
240
50
32
----
322