Find the value of a3-a2-a-1- where -a- satisfies the equation - 4 x-3-2 x-7-2 x-7-x-2

The correct option is C 104 4x+3/2x+7=2x 7/x+2 ∵ 'a' satisfies the equation 4a+3/2a+7=2a 7/a+2 ⇒ (4a+3)(a+2)=(2a 7)(2a+7) ⇒ 4a(a+2)+3(a+2)=(2a)^2 (7)^2 ⇒ 4a ...

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Quantitative Aptitude

Quadratic Equations

Find the valu...

Question

$Find the value of a^{3} + a^{2} + a + 1, where 'a' satisfies the equation : \frac{4 x + 3}{2 x + 7} = \frac{2 x - 7}{x + 2}$

-5

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-49

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-88

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-104

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Solution

The correct option is D
-104

$\frac{4 x + 3}{2 x + 7} = \frac{2 x - 7}{x + 2} ∵'a' satisfies the equation \frac{4 a + 3}{2 a + 7} = \frac{2 a - 7}{a + 2} \Rightarrow (4 a + 3) (a + 2) = (2 a - 7) (2 a + 7) \Rightarrow 4 a (a + 2) + 3 (a + 2) = (2 a)^{2} - (7)^{2} \Rightarrow 4 a^{2} + 8 a + 3 a + 6 = - 49 \Rightarrow 11 a = - 55 \Rightarrow a = - 5 N o w, a^{3} + a^{2} + a + 1 = (- 5)^{3} + (- 5)^{2} - 5 + 1 = - 125 + 25 - 5 + 1 = - 105 + 1 = - 104$

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Find the value of a3+a2+a+1,where 'a' satisfies the equation : 4x+32x+7=2x−7x+2

The correct option is D -104 4x+32x+7=2x−7x+2∵ 'a' satisfies the equation4a+32a+7=2a−7a+2⇒(4a+3)(a+2)=(2a−7)(2a+7)⇒4a(a+2)+3(a+2)=(2a)2−(7)2⇒4a2+8a+3a+6=−49⇒11a=−55⇒a=−5Now, a3+a2+a+1=(−5)3+(−5)2−5+1 =−125+25−5+1 =−105+1=−104

$Find the value of a^{3} + a^{2} + a + 1, where 'a' satisfies the equation : \frac{4 x + 3}{2 x + 7} = \frac{2 x - 7}{x + 2}$