Question

If a+b=1 and a^2+b^2=2 then what is the value of a^5+b^5 (where a and b are real numbers) ?

Answer 1

Answer:

now use

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

we have a+b =1 and a^{2}  +b^{2} = 2

then

(1)^{2} = 2 +2 a b

1 -2 = 2 ab

-1 =2 ab

-1/2 =ab  then a = -1/2b

put value of a in a+b =1

-1/2b +b =1 by solving quadratic equation

then value of  b  is 1+ $\sqrt{2$ /2 and 1 -$\sqrt{2}$ /2

and value of a is  -1- $\sqrt{2$   and-1 +$\sqrt{2}$

by this value find a^5+b^5

Step-by-step explanation: