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Algebra Level 4

If x = 3 − 4 i x = 3 - 4i , then what is the value of x 4 − 10 x 3 + 74 x 2 − 250 x + 629 x^4 - 10 x^3 + 74 x^2 - 250 x + 629 ?

Clarification : i = − 1 i=\sqrt{-1} .


The answer is 4.

Samara Simha Reddy by Samara Simha Reddy , 22, India

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1 solution

x = 3 − 4 i \large x = 3 - 4i

⟹ x − 3 = − 4 i \large \implies x - 3 = -4i

"By Squaring on Both the sides."

( x − 3 ) 2 = − 16 \large (x - 3)^2 = -16 ............. [ ∵ i 2 = − 1 \because i^2 = -1 ]

⟹ x 2 − 6 x + 25 = 0 \large \implies x^2 - 6 x + 25 = 0

The equation x 4 − 10 x 3 + 74 x 2 − 250 x + 629 \large x^4 - 10 x^3 + 74 x^2 - 250 x + 629 can be expressed as,

x 2 ( x 2 − 6 x + 25 ) − 4 x ( x 2 − 6 x + 25 ) + 25 ( x 2 − 6 x + 25 ) + 4 \large x^2(x^2 - 6x + 25) - 4x(x^2 - 6x + 25) + 25(x^2 - 6x + 25) + 4

= x 2 ( 0 ) − 4 x ( 0 ) + 25 ( 0 ) + 4 \large = x^2(0) - 4x(0) + 25(0) + 4

= 4 \large = \boxed{4}

∴ \therefore The answer for the above expression is 4 \boxed4

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Same way ! (+1)

Aditya Sky - 5 years, 2 months ago

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