Evaluate the mentioned below-i2-3-2-2-7-72 -when -3-5-2

Given that 𝑥=3−5𝑖2 ⇒ 2𝑥−3=−5𝑖 ⇒(2𝑥−3)^2=(−5𝑖)^2 nbsp; squaring on both sides ⇒4𝑥^2−12𝑥+9=25𝑖^2 ⇒4𝑥^2−12𝑥+9=25 × (−1) ⇒ 2𝑥^2−6𝑥+17=0 nbsp; nbsp; …(1) ⇒ ...

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Standard XII

Mathematics

How to Find the Inverse of a Function

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Question

Evaluate the mentioned below:
(i) $2 x^{3} + 2 x^{2} - 7 x + 72, w h e n x = \frac{3 - 5 i}{2}$

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Solution

Given that-
$x = \frac{3 - 5 i}{2}$
$\Rightarrow 2 x - 3 = - 5 i$
$\Rightarrow (2 x - 3)^{2} = (- 5 i)^{2} s q u a r i n g o n b o t h s i d e s$
$\Rightarrow 4 x^{2} - 12 x + 9 = 25 i^{2}$
$\Rightarrow 4 x^{2} - 12 x + 9 = 25 \times (- 1)$
$\Rightarrow 2 x^{2} - 6 x + 17 = 0 \dots (1)$
$\Rightarrow 2 x^{3} + 2 x^{2} - 7 x + 72$
$= x (2 x^{2} - 6 x + 17) + 8 x^{2} - 24 x + 72$
$= x (2 x^{2} - 6 x + 17) + 4 (2 x^{2} - 6 x + 17) + 4$
$= x \times 0 + 4 \times 0 + 4$ {from eqn (1)}
$= 4$
$∴ 2 x^{3} + 2 x^{2} - 7 x + 72 = 4$

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How to Find the Inverse of a Function

Standard XII Mathematics

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Evaluate the mentioned below: (i)2x3+2x2−7x+72,when x=3−5i2

Given that- x=3−5i2 ⇒2x−3=−5i ⇒(2x−3)2=(−5i)2squaring on both sides ⇒4x2−12x+9=25i2 ⇒4x2−12x+9=25×(−1) ⇒2x2−6x+17=0…(1) ⇒2x3+2x2−7x+72 =x(2x2−6x+17)+8x2−24x+72 =x(2x2−6x+17)+4(2x2−6x+17)+4 =x×0+4×0+4 {from eqn (1)} =4 ∴2x3+2x2−7x+72=4

Evaluate the mentioned below:
(i) $2 x^{3} + 2 x^{2} - 7 x + 72, w h e n x = \frac{3 - 5 i}{2}$