If x3+4=x2+312, then the value of x is

When x = 1x3+4=x2+31213+41=12+721+123=1+72133=82When x = 12x3+41=x2+312123+41=122+3124+4=6+728=192 L.H.S ≠ R.H.S When x= -12x3+4=x2+312−123+4=−122+72−1+246=1+144236=154 L.H.S ≠R.H.SWhen x= 3x3+4=x2+31233+4=32+721+4=3+725=5 L.H.S = R.H.S ∴ The value of x is ' 3 '

If x3+4=x2+312, then the value of x is

When x = 1x3+4=x2+31213+41=12+721+123=1+72133=82When x = 12x3+41=x2+312123+41=122+3124+4=6+728=192 L.H.S ≠ R.H.S When x= -12x3+4=x2+312−123+4=−122+72−1+246=1+144236=154 L.H.S ≠R.H.SWhen x= 3x3+4=x2+31233+4=32+721+4=3+725=5 L.H.S = R.H.S ∴ The value of x is ' 3 '

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If $\frac{x}{3} + 4 = \frac{x}{2} + 3 \frac{1}{2}$ , then the value of x is

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- $\frac{1}{2}$

answer is D.

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Detailed Solution

When x = 1
$\begin{aligned} \frac{x}{3} + 4 = \frac{x}{2} + 3 \frac{1}{2} \\ \frac{1}{3} + \frac{4}{1} = \frac{1}{2} + \frac{7}{2} \\ \frac{1 + 12}{3} = \frac{1 + 7}{2} \\ \frac{13}{3} = \frac{8}{2} \end{aligned}$
When x = 12
$\begin{array}{l} \frac{x}{3} + \frac{4}{1} = \frac{x}{2} + 3 \frac{1}{2} \\ \frac{12}{3} + \frac{4}{1} = \frac{12}{2} + 3 \frac{1}{2} \\ 4 + 4 = 6 + \frac{7}{2} \\ 8 = \frac{19}{2} L.H.S \neq R.H.S \end{array}$

When x= - $\frac{1}{2}$
$\begin{array}{l} \frac{x}{3} + 4 = \frac{x}{2} + 3 \frac{1}{2} \\ \frac{(- \frac{1}{2})}{3} + 4 = \frac{(\frac{- 1}{2})}{2} + \frac{7}{2} \\ \frac{- 1 + 24}{6} = \frac{1 + 14}{4} \\ \frac{23}{6} = \frac{15}{4} L.H.S \neq R . H . S \end{array}$

When x= 3
$\begin{array}{l} \frac{x}{3} + 4 = \frac{x}{2} + 3 \frac{1}{2} \\ \frac{3}{3} + 4 = \frac{3}{2} + \frac{7}{2} \\ 1 + 4 = \frac{3 + 7}{2} \\ 5 = 5 L.H.S = R.H.S \\ ∴ The value of x is ' 3' \end{array}$