If 2 a -3- a -1- then- the value of 8 a 3-27- a 3 is not equal to 18 -A- TrueB- False

The correct option is A True Given: 2a 3/a=1 ⇒(2a 3/a)^3=1 ⇒ (2a)^3 3^3/a^3 3× 2a×3/a×(2a 3/a)=1 ⇒ 8a^3 27/a^3 18×1=1 ⇒ 8a^3 27/a^3=1+18=19 Therefore, the valu ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identity: (a - b)(a + b) = a^2 - b^2

If 2 a -3/ a ...

Question

If $2 a - \frac{3}{a} = 1$ , then, the value of $8 a^{3} - \frac{27}{a^{3}}$ is not equal to 18 .

True

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False

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Solution

The correct option is A
True

Given: $2 a - \frac{3}{a} = 1$

$\Rightarrow {(2 a - \frac{3}{a})}^{3} = 1$

$\Rightarrow (2 a)^{3} - \frac{3^{3}}{a^{3}} - 3 \times 2 a \times \frac{3}{a} \times (2 a - \frac{3}{a}) = 1$

$\Rightarrow 8 a^{3} - \frac{27}{a^{3}} - 18 \times 1 = 1$

$\Rightarrow 8 a^{3} - \frac{27}{a^{3}} = 1 + 18 = 19$

Therefore, the value is 19 and not 18.

Hence the statement is true.

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If $2 a - \frac{3}{a} = 1$ , then, the value of $8 a^{3} - \frac{27}{a^{3}}$ is not equal to 18 .

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If 2a−3a=1, then, the value of 8a3−27a3 is not equal to 18 .

The correct option is A True Given: 2a−3a=1 ⇒(2a−3a)3=1 ⇒(2a)3−33a3−3×2a×3a×(2a−3a)=1 ⇒8a3−27a3−18×1=1 ⇒8a3−27a3=1+18=19 Therefore, the value is 19 and not 18. Hence the statement is true.

If $2 a - \frac{3}{a} = 1$ , then, the value of $8 a^{3} - \frac{27}{a^{3}}$ is not equal to 18 .