Find x if 8 x3-2 x -28 x2-1-35-19A- 2-5B- 4-5C- 10D- 6

The correct option is A 2.5 Given that 8x^3 + 6x/12x^2 +1 = 35/19 Applying componendo dividendo, 8x^3 + 6x+12x^2 +1/8x^3 + 6x 12x^2 1 = 35+19/35 19 i.e., (2x+ ...

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Byju's Answer

Standard IX

Mathematics

Application of Direct Proportionality

Find x if 8 x...

Question

Find $x$ if $\frac{8 x^{3} + 6 x}{12 x^{2} + 1} = \frac{35}{19}$

2.5

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Solution

The correct option is A
2.5

Given that $\frac{8 x^{3} + 6 x}{12 x^{2} + 1} = \frac{35}{19}$

Applying componendo dividendo, $\frac{8 x^{3} + 6 x + 12 x^{2} + 1}{8 x^{3} + 6 x - 12 x^{2} - 1} = \frac{35 + 19}{35 - 19}$

i.e., $\frac{(2 x + 1)^{3}}{(2 x - 1)^{3}} = \frac{54}{16} = \frac{27}{8} = \frac{3^{3}}{2^{3}}$

$⟹ \frac{2 x + 1}{2 x - 1} = \frac{3}{2}$

$⟹ 4 x + 2 = 6 x - 3$

$⟹ 2 x = 5$

Thus, $x = 2.5$

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Find x if 8x3+6x12x2+1=3519

The correct option is A 2.5 Given that 8x3+6x12x2+1=3519 Applying componendo dividendo, 8x3+6x+12x2+18x3+6x−12x2−1=35+1935−19 i.e., (2x+1)3(2x−1)3=5416=278=3323 ⟹2x+12x−1=32 ⟹4x+2=6x−3 ⟹2x=5 Thus, x=2.5

Find $x$ if $\frac{8 x^{3} + 6 x}{12 x^{2} + 1} = \frac{35}{19}$