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Properties of Inverse Function

If 3x+4 2+ ...

Question

If ${(3 x + 4)}^{2} + {(3 x - 2)}^{2} = (6 x + 5) (3 x - 2) + 12$ , then the value of x is

A

2

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B

1

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C

-3

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D

-2

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Solution

The correct option is D -2
The given equation is
${(3 x + 4)}^{2} + {(3 x - 2)}^{2} = (6 x + 5) (3 x - 2) + 12 ⟹ 9 x^{2} + 16 + 24 x + 9 x^{2} + 4 - 12 x = 18 x^{2} + 15 x - 12 x - 10 + 12 ⟹ 12 x + 20 = 3 x + 2 ⟹ 9 x = - 18 ⟹ x = - 2$
Ans- Option D.

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\frac{2}{3 x + 12} = \frac{2}{3}

, then the value of

x + 4

${lim}_{x \to \infty} {\frac{x^{2} + 2 x + 3}{2 x^{2} + x + 5}}^{\frac{3 x - 2}{3 x + 2}}$

∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{2} + x & x + 1 & x - 2 2 x^{2} + 3 x - 1 & 3 x & 3 x - 3 x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = A x - 12

, then the value of

A

∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{2} + x & x + 1 & x - 2 {2 x}^{2} + 3 x - 1 & 3 x & 3 x - 3 x^{2} + 2 x + 3 & 2 x - 1 & 2 x - 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = a x - 12,

a^{2}

y = 3 x + 6 x^{2} + 10 x^{3} + . . .

then the value of

x

y

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