Question

Suppose a+b=1 and a² +b²=3.
Find the value of A power 5 + b ki power 5 =?​

Answer 1

Answer:

11

Step-by-step explanation:

${(a + b)}^{5} = {a}^{5} + {b}^{5} + 5ab({a}^{3} + {b}^{3} + 2ab(a + b))$

As we have (a+b) =1,

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

And

${a}^{2} + {b}^{2} = 3$

Hence

${1}^{2} = 3 + 2ab$

$2ab = - 2 \\ ab = - 1$

Now as we know

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b)$

Hence by putting values, (a+b) =1, ab= -1 we get

${1}^{3} = {a}^{3} + {b}^{3} + 3( - 1)(1) \\ {a}^{3} + {b}^{3} = 1 + 3 \\ {a}^{3} + {b}^{3} = 4$

Now in our final equation,

By putting all values we get,

${1}^{5} = {a}^{5} + {b}^{5} + 5( - 1)(4 + 2( - 1)(1)) \\ {a}^{5} + {b}^{5} = 1 + 10 \\ {a}^{5} + {b}^{5} = 11 \\ \\ as \\ {a}^{3} + {b}^{3} = 4 \\ ab = ( - 1)and \\ (a + b) = 1$

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