If x3 - 4x2 + 19 = 6(x - 1) then what is the value of $$\left[ {{x^2} + \frac{1}{{x - 4}}} \right]?$$
A. 3
B. 5
C. 6
D. 8
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & {x^3} - 4{x^2} + 19 = 6\left( {x - 1} \right)......\left( 1 \right)\left( {{\text{Given}}} \right) \cr & \& \,\left( {{x^2} + \frac{1}{{x - 4}}} \right) = ?\left( {{\text{To find}}} \right) \cr & \to \frac{{{x^2}\left( {x - 4} \right) + 1}}{{x - 4}}......\left( 2 \right) \cr & {\text{from equation}}\left( 1 \right) \cr & {x^3} - 4{x^2} + 19 = 6x - 6 \cr & {x^3} - 4{x^2} + 1 + 18 = 6x - 6 \cr & {x^3} - 4{x^2} + 1 = 6x - 6 - 18 \cr & {x^3} - 4{x^2} + 1 = 6x - 24 \cr & {\text{putting the value of }}\left( {{x^3} - 4{x^2} + 1} \right){\text{in equation }}\left( 2 \right) \cr & {\text{we get,}} = \frac{{6x - 24}}{{x - 4}} = \frac{{6\left( {x - 4} \right)}}{{\left( {x - 4} \right)}} = 6 \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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