Question

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

Step-by-step explanation:

$\red{\bold{\underline{\underline{QUESTION:-}}}}$

Q:-solve and verify the equation

$\frac{1}{2} - \frac{1}{3} (x - 1) + 2 = 0$

$\huge\tt\underline\blue{Answer }$

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$⟹ \frac{1}{2} - \frac{1}{3} (x - 1) + 2 = 0</p><p>$

$⟹</p><p> \frac{3 - 2(x - 1) + 2}{6} = 0$

$⟹</p><p> \frac{1}{6} (x - 1) + 2 = 0$

$⟹</p><p>(x - 1) + 2 = 0$

$⟹</p><p>x - 1 = - 2$

$⟹</p><p>x = - 2 + 1$

$⟹</p><p>x = - 1$

CHECK:-

$⟹ \frac{1}{2} - \frac{1}{3} ( - 1 - 1) + 2</p><p>$

$⟹</p><p> \frac{3 - 2( - 2) + 2}{6} = 0$

$⟹</p><p> \frac{1}{6} ( - 2) + 2 = 0$

$⟹</p><p> \frac{0}{6} = 0$

$⟹</p><p>0 = 0$

THEREFORE,L.H.S=R.H.S

VERIFIED ✔️

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HOPE IT HELPS YOU..

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Answer 2

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.