If a+b+c=4
a2+b2+c2=10
a3+b3+c3=22
Find a4+b4+c4
Answers
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
Answer:
15
Step-by-step explanation:
a4+b4+c4=15 a4=5 b4=6 c4=5