Which of the following equations is NOT equivalent to $10 y^{2} = (x + 2) (x - 2)$ ?

30 y^{2} = 3 x^{2} - 12

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20 y^{2} = (2 x - 4) (x + 2)

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{10 y}^{2} + 4 = x^{2}

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5 y^{2} = x^{2} - 2

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y^{2} = \frac{x^{2} - 4}{10}

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Solution

The correct option is C $5 y^{2} = x^{2} - 2$
$10 y^{2} = (x + 2) (x - 2) = x^{2} - 4$
so when multiplied by 3 we get (A)
so when multiplied by 2 we get (B)
so when multiplied by 0.1 we get (E)
als adding 4 on both sides we get (C)
option (D) is not got by any manipulation

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Question 10
Which of the following equations has no real roots?
(A) $x^{2} - 4 x + 3 \sqrt{2} = 0$
(B) $x^{2} + 4 x - 3 \sqrt{2} = 0$
(C) $x^{2} - 4 x - 3 \sqrt{2} = 0$
(D) $3 x^{2} - 4 \sqrt{3} x + 4 = 0$

Q. FInd

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for which

∣ ∣ ∣ \frac{x^{2} - 2 x + 1}{x^{2} - 4 x + 4} ∣ ∣ ∣ + ∣ ∣ ∣ \frac{x - 1}{x - 2} ∣ ∣ ∣ - 12 < 0

Question 2
Which of the following is not a quadratic equation?
(a) $2 (x - 1)^{2} = 4 x^{2} - 2 x + 1$
(b) $2 x - x^{2} = x^{2} + 5$
(c) ${(\sqrt{2} x + \sqrt{3})}^{2} = 3 x^{2} - 5 x$
(d) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{3}$