1- 3x -20x-32-011II- 2 y- -3y-20-01

The correct option is E x ≥ yEquation I 3x^2 20x 32=0 ⇒ 3x^2 12x 8x 32=0 ⇒ 3x(x 4) 8(x 4)=0 ⇒ (3x 8)(x 4)=0 ∴ x=8/3, 4 Equation II 2y^2 3y 20=0 ⇒ 2y^2 8y+5y 20 ...

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Standard XII

Mathematics

Derivative of Standard Functions

1. 3x -20x-32...

Question

$I . 3 x^{2} - 20 x - 32 = 0 I I . 2 y^{2} - 3 y - 20 = 0$

x < y

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x \leq y

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x > y

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Realtionship between x and y cannot be established

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x \geq y

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Solution

The correct option is E $x \geq y$
Equation I
$3 x^{2} - 20 x - 32 = 0$
$\Rightarrow 3 x^{2} - 12 x - 8 x - 32 = 0$
$\Rightarrow 3 x (x - 4) - 8 (x - 4) = 0$
$\Rightarrow (3 x - 8) (x - 4) = 0$
$∴ x = \frac{8}{3}, 4$
Equation II
$2 y^{2} - 3 y - 20 = 0$
$\Rightarrow 2 y^{2} - 8 y + 5 y - 20 = 0$
$\Rightarrow 2 y (y - 4) + 5 (y - 4) = 0$
$\Rightarrow (2 y + 5) (y - 4) = 0$
$∴ y = 4, - \frac{5}{2}$
Hence, $x \geq y$

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I. 3x2−20x−32=0II. 2y2−3y−20=0

The correct option is E x≥yEquation I 3x2−20x−32=0 ⇒3x2−12x−8x−32=0 ⇒3x(x−4)−8(x−4)=0 ⇒(3x−8)(x−4)=0 ∴x=83,4 Equation II 2y2−3y−20=0 ⇒2y2−8y+5y−20=0 ⇒2y(y−4)+5(y−4)=0 ⇒(2y+5)(y−4)=0 ∴y=4,−52 Hence, x≥y

$I . 3 x^{2} - 20 x - 32 = 0 I I . 2 y^{2} - 3 y - 20 = 0$