Math, asked by kumarisamiksha785, 1 month ago

a+b+c = 4
a²+b²+c²=10
a³+b³+c³=22
a⁴+b⁴+c⁴=
what is the answer please tell thise who will solve right i will give thans and marks as brainlist answer​

Answers

Answered by JigyashaJain
0

Answer:

a⁴+b⁴+c⁴ = 50

Step-by-step explanation:

a + b + c = 4_________(1)

a²+b²+c²=10________(2)

a³+b³+c³=22________(3)

Taking eq. 1

a + b + c = 4

Squaring both sides

(a+b+c)² = 4²

a²+b²+c²+2ab+2bc+2ca = 16

a²+b²+c²+2(ab+bc+ca) = 16

From eq. 2, putting value of a²+b²+c²

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

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

2(ab+bc+ca) = 6

(ab+bc+ca) = 6/2

(ab+bc+ca) = 3______________(4)

Multiplying eq. 1 and 2

a+b+c = 4

a²+b²+c² = 10

a³+ab²+ac²+ba²+b³+bc²+ca²+cb²+c³ = 40

a³+b³+c³+ab²+ac²+ba²+bc²+ca²+cb² = 40

Putting value of a³+b³+c³ given in eq. 3

= 22+ab²+ac²+ba²+bc²+ca²+cb² = 40

= ab²+ac²+ba²+bc²+ca²+cb² = 40-22

= ab²+ac²+ba²+bc²+ca²+cb² = 18____(5)

Taking eq. 2,

a²+b²+c² = 10

Squaring both sides

(a²+b²+c²)² = 10²

= a⁴+b⁴+c⁴+2a²b²+2b²c²+2c²a² = 100

= a⁴+b⁴+c⁴+2(a²b²+b²c²+c²a²) = 100____(6)

Multiplying eq. 1 and 4

a+b+c = 4

(ab+bc+ca) = 3

= a²b+abc+a²c+ab²+b²c+abc+abc+bc²+c²a = 12

= a²b+a²c+ab²+b²c+bc²+c²a+3abc = 12

Putting value of ab²+ac²+ba²+bc²+ca²+cb² given in eq. 5

= 18 + 3abc = 12

3abc = 12-18

3abc = -6

abc = -6/3

abc = -2

Squaring eq. 4

= (ab+bc+ca) = 3

= (ab+bc+ca)² = 3²

= a²b²+b²c²+c²a²+2ab²c+2bc²a+2cba² = 9

= a²b²+b²c²+c²a²+2(ab²c+abc²+a²bc) = 9

= a²b²+b²c²+c²a²+2×abc(b+c+a) = 9

Putting value of abc and a+b+c from eq.

= a²b²+b²c²+c²a²+2×-2(4) = 9

= a²b²+b²c²+c²a²-16 = 9

= a²b²+b²c²+c²a² = 9+16

= a²b²+b²c²+c²a² = 25______(7)

Putting value of eq. 7 in eq. 6

= a⁴+b⁴+c⁴+2(a²b²+b²c²+c²a²) = 100

= a⁴+b⁴+c⁴+2(25) = 100

= a⁴+b⁴+c⁴+50 = 100

= a⁴+b⁴+c⁴ = 100-50

= a⁴+b⁴+c⁴ = 50

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