Question

If X=(-1)¹ + (−1)² + (-1)³ + (-1) +...25 terms, Y =(-1)-(-1) + (-1)³ −(−1)¹ +...25 terms. Then X² +Y² is​

Answer 1

Step-by-step explanation:

step-by-step explanation

Answer 2

The value of X²+Y² is 626.

Given:

X=(-1)¹ + (−1)² + (-1)³ + (-1) +...25 terms.

Y =(-1)-(-1) + (-1)³ −(−1)¹ +...25 terms.

To Find:

The value of X²+Y².

Solution:

For the value of 'X',

The series given for X is the value of the addition of the consecutive power of -1 till 25.

As even power will add a positive one and the odd power will add a negative one.

So, the value for X is,

                                   $X = 12-13\\X = -1$

For the value of 'Y',

The series given for Y is the value of the addition of the formatted power of -1 till 25.

As every third power will add a negative one and rest of all will also do the same.

So, the value for Y is,

                                      $Y = -25$

Now the value of X²+Y² is,

                            $X^2+Y^2=(-1)^2+(-25)^2\\~~~~~~~~~~~~=~1+625\\~~~~~~~~~~~~=~626$

Hence the value of X²+Y² is 626.