a+b+c=4, a2+b2+c2=10, a3+b3+c3=22 ,a4+b4+c4=?

Question

a+b+c=4, a2+b2+c2=10, a3+b3+c3=22 ,a4+b4+c4=?

in progress 0
Eloise 7 months 2021-10-07T22:59:57+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-10-07T23:01:07+00:00

    Given :

    a+b+c=4,

    a²+b²+c²=10,

    a³+b³+c³ = 22

    To Find : a⁴+b⁴+c⁴=?

    Solution:

    a+b+c=4

    Squaring both sides

    => a²+b²+c²  + 2(ab + bc + ca) = 16

    => 10 + 2(ab + bc + ca) = 16

    => ab + bc + ca = 3

    a³+b³+c³  – 3abc  = (a + b + c)(a²+b²+c² – ( ab + bc + ca))

    => 22 – 3abc = (4)(10 – 3)

    => 22 – 3abc = 28

    => 3abc = – 6

    => abc = – 2

    ab + bc + ca = 3

    Squaring both sides

    => (ab)² + (bc)² + (ac)² + 2(ab.bc + ab.ca + bc.ca)  = 9

    =>  (ab)² + (bc)² + (ac)²  + 2abc(a + b + c)  = 9

    => (ab)² + (bc)² + (ac)²  + 2(-2)(4)  = 9

    =>  (ab)² + (bc)² + (ac)² = 25

    => a²b² + b²c² + a²c² = 25

    a²+b²+c²=10

    squaring both sides

    => a⁴ + b⁴ + c⁴  + 2( a²b² + b²c² + a²c²) = 100

    => a⁴ + b⁴ + c⁴  + 2( 25) = 100

    => a⁴ + b⁴ + c⁴  + 50 = 100

    =>  a⁴ + b⁴ + c⁴ = 50

    Learn More:

    a³ + b³ + c³ -3abc = ( a + b + c)(a² + b² + c² – ab – bc – ca) .

    brainly.in/question/1195178

    If a+b+c=6 and a2+b2+c2=14 and a3+b3+c3=36 find value of abc …

    https://brainly.in/question/11392304

Leave an answer

Browse
Browse

18:9+8+9*3-7:3-1*13 = ? ( )