Question

find the value of 2x²+5x³+7x²-x+41,when x=-2- .

i
$\sqrt{3}$
​

Answer 1

Answer:

ANSWER

2x

4

+5x

3

+4x

2

−x+41 ---(1)

when x=−2−

3

i=−(2+

3

i)---(2)

x

2

=(2+

3

i)

2

=4+3(i)

2

+4

3

i

=4−3+4

3

! (∵i

2

=−1)

x

2

=1+4

3

i ---(3)

x

3

=x

2

.x

=(1+4

3

i)[−(2+

3

i)]

=−(2+

3

i+8

3

i+12!

2

)

=−(2−12+9

3

i)

x

3

=10−9

3

i ---(4)

x

4

=(x

2

)

2

=(1+4

3

i)

2

=1+48!

2

+8i

3

=1−48+8i

3

(i

2

=−1)

x

4

=−47+8!

3

---(5)

From (1),(2),(3),(4) and (5)

2(−47+8i

3

)+5(10−9

3

i)+7(1+4

3

i)−(−2

3

i)+41 −94+16i

3

+50−45

3

i+7+28

3

i+2+

3

i+41

=6 d)

solution