Question

Find the subset of the following which has been given in the picture above...
Both Q.no.6 and 7


{ Wrong answers will be reported}​

Answer 1

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$\small\underline\bold\red{Question-}$

• $\sqrt[3]{x} + 2 \sqrt[3]{ {x}^{2} } = 3$

$\small\underline\bold\red{To\:Find-}$

• $Value\:of\:x$

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▪️ Let $\sqrt[3]{x}$ = $a$

2a² + a - 3 = 0

$\implies$ 2 ${a}^{2}$-$2a$+ $3a$-3 = 0

$\implies$ 2$a$($a$-1)+3($a$-1) = 0

$\implies$ $(a-1)$$(2a+3)$ = 0

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Hence,

$(a-1)$ = 0

$\implies$ a = 1

$\implies$ $\sqrt[3]{x}$ = 1

$\implies$ $x$ = (1)³ = 1

or,

$(2a+3)$ = 0

$\implies$ a = $\frac{-3}{2}$

$\implies$ $\sqrt[3]{x}$ = $\frac{-3}{2}$

$\implies$ $x$ = ${( \frac{ - 3}{2} )}^{3}$ = $\frac{-27}{8}$

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∴ x ∈ { 1,$\frac{-27}{8}$ }

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Answer 2

Answer:

$\huge\fcolorbox{white}{red}{Hello Ankesh}$

Question−

[3]{x} + 2 [3]{ {x}^{2} } = 3

3

x

+2

3

x

2

=3

ToFind−

Value of x

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▪️ Let[3]{x}

3

x

= aa

2a² + a - 3 = 0

2 {a}^{2}a

2

-2a^2 + 3a -3 = 0

2a (a -1)+3(a-1) = 0

(a-1)(a−1) (2a+3)(2a+3) = 0

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Hence,

(a-1)(a−1) = 0

a = 1

[3]{x}

3

x

= 1

x = (1)³ = 1

or,

(2a+3)(2a+3) = 0

\implies⟹ a = \frac{-3}{2}

2

−3

[3]{x}

3

x

= {-3}{2}

2

−3

⟹ xx = { - 3}{2} )}^{3}(

2

−3

)

3

= \frac{-27}{8}

8

−27

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∴ x ∈ { 1,{-27}{8}

8

−27

}

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