Question

(-2)^5+(-1/3)^4:find the value
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Answer 1

Answer:- 1

Step-by-step explanation:- We know (A+B)^3 = A^3 + B^3 + 3AB(A+B)

Now put A=( 2+√5 )^1/3 and B=( 2-√5 )^1/3

So now after substituting we have

{ (2+√5 )^1/3 + (2-√5)^1/3 }^3

= 2+√5 +2 -√5 + 3(2+√5)(2-√5)[ (2+√5 )^1/3 + (2-√5)^1/3) ]

You want to find ( 2+√5 )^1/3 + ( 2-√5 )^1/3

let’s take it as X

Now it is X^3 = 4 + 3*(2+√5)(2-√5)*X

i.e. X^3 = 4 + 3*(4-5)*X

i.e. X^3 = 4 - 3*X

This cubic equation has only one real solution which is “1”.

So, [ ( 2+√5 )^1/3 + ( 2-√5 )^1/3 ] = 1

Answer 2

(-2)^5 + (-1/3)^4

we know that 2^5 = 32 but since it's -2^5 it will be -32 being the exponential operation of odd no I.e 5.

and we know (1/3)^4 = 1/81 and this will remain as positive because the exponential operation is of an even no. i.e 4

Solve :

-32 + 1/81

1/81 - 32

(1- 2592)/ 81

- 2591/81

= 31 . 987

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