Question

Q:-solve this equation and also verify........._______........
$\frac{1}{2} - \frac{1}{3} (x - 1) + 2 = 0$
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Answer 1

Answer:

Given equation is x 2/3 + x 1/3 - 2 = 0

Putting x 1/3 = y, the given equation becomes

y2 + y – 2 = 0

⇒ y2 + 2y – y – 2 = 0

⇒ y(y+ 2) – 1(y + 2) = 0

⇒ (y + 2) (y – 1) = 0

⇒ y + 2 = 0 or y – 1 = 0

⇒ y = -2 or y = 1

But x 1/3 = y

∴ x 1/3 = - 2 or x 1/3 = 1

⇒ x = (- 2)3 or x = (1)3

⇒ x = - 8 or x = 1

Hence, roots are -8, 1.

Answer 2

Working out:

Here we are provided with an equation in variable x. And we have to find the value of this variable x in this equation.

GiveN:

• $\sf{ \dfrac{1}{2} - \dfrac{1}{3} (x - 1) + 2 = 0}$

So, let's start solving the above equation and understand the steps of solving to reach the final result.

$\sf{ \longrightarrow{ \dfrac{1}{2} - \dfrac{1}{3} (x - 1) + 2 = 0}}$

Opening the parentheses,

$\sf{ \longrightarrow{ \dfrac{1}{2} - \dfrac{1}{3}x + \dfrac{1}{3} + 2 = 0}}$

Now combining and adding the constant and the like terms in this equation:

$\sf{ \longrightarrow{ \dfrac{1}{2} + \dfrac{1}{3} + 2 - \dfrac{1}{3}x = 0}}$

$\sf{ \longrightarrow{ \dfrac{3 + 2 + 12}{6} - \dfrac{1}{3}x = 0}}$

$\sf{ \longrightarrow{ \dfrac{17}{6} = \dfrac{1}{3} x}}$

Now we have to find x, so let's flip the equation:

$\sf{ \longrightarrow{ \dfrac{1}{3}x = \dfrac{17}{6} }}$

We know that inverse of division is multiplication, hence we can multiply 3 in RHS,

$\sf{ \longrightarrow{x = \dfrac{17}{6} \times 3}}$

$\sf{ \longrightarrow{x = \dfrac{17}{2}}}$

Hence the required value for x is:

$\huge{ \boxed{ \sf{ \red{x = \dfrac{17}{2} }}}}$

And we are done !!

Quick verification:

Let's plug in the value of x in the equation,

$\sf{ \longrightarrow{ \dfrac{1}{2} - \dfrac{1}{3} ( \dfrac{17}{2} - 1) + 2 = 0}}$

$\sf{ \longrightarrow{ \dfrac{1}{2} - \dfrac{1}{3} ( \dfrac{15}{2} ) + 2 = 0}}$

$\sf{ \longrightarrow{ \dfrac{1}{2} - \dfrac{5}{2} + 2 = 0}}$

$\sf{ \longrightarrow{ \dfrac{ - 4}{2} + 2 = 0}}$

$\sf{ \longrightarrow{0 = 0}}$

Here, LHS = RHS

✤ Hence, verified !!