Question

FIND THE REQUIRED VALUE OF EXPRESSION IN THE GIVEN ATTACHMENT

★ CONTENT QUALITY ANSWER REQUIRED ★

Answer 1

Hey THEBRAINLY1,

It's a very long question so please stay with me!!!!

(a+b+c)²=6²
a²+b²+c²+2(ab+bc=ca)=36
Since a²+b²+c²=14, so let's put it in the equation, we get-
14+2(ab+bc+ca)=36
2(ab+bc+ca)=22
So ab+bc+ca=11----EQUATION 1

Now, there's a theorem that-
a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-bc-ca)
Since a³+b³+c³=36
a²+b²+c²=14
a+b+c=6,and
ab+bc+ca=11----(EQUATION 1)

So lets assign the values in the equation-
36-3abc=6(14-11)
36-3abc=18
Cancelling 3, we get-
12-abc=6
So abc=6----EQUATION 2

Now stay with me, I am doing this operation just to the value of an expression which is about to come.

(ab+bc+ca)²=a²b²+b²c²+c²a²+2(a²bc+ab²c+abc²)
(11)²=a²b²+b²c²+c²a²+2abc(a+b+c)
121=a²b²+b²c²+c²a²+12(6)
a²b²+b²c²+c²a²=49----EQUATION 3

Now let's square a²+b²+c², we get-
(a²+b²+c²)²=a⁴+b⁴+c⁴+2(a²b²+b²c²+c²a²)
Assigning all the values, we get-
a⁴+b⁴+c⁴=196-2(49)
a⁴+b⁴+c⁴=196-98

a⁴+b⁴+c⁴=98

PLEASE MARK AS BRAINLIEST IF HELPFUL!!!
(I HAVE SERIOUSLY DONE SOME HARD WORK)

Regards
07161020
Brainly Star
Ace