Assertion and Reason Question on Algebraic Identities
Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct answer.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) Statement-1 is false, Statement-2 is true.
Statement-1 (Assertion):
The value of \[ \frac{(0.027)^3+(0.023)^3} {(0.027)^2-(0.027)(0.023)+(0.023)^2} \] is \[ 0.05 \]
Statement-2 (Reason):
\[ a^3-b^3 = (a-b)(a^2-ab+b^2) \]
Solution
Using identity:
\[ a^3+b^3 = (a+b)(a^2-ab+b^2) \]
Therefore,
\[ \frac{(0.027)^3+(0.023)^3} {(0.027)^2-(0.027)(0.023)+(0.023)^2} \]
\[ =0.027+0.023 \]
\[ =0.05 \]
Hence, Statement-1 is true.
Statement-2 is also true, but it is not the correct explanation for Statement-1 because Statement-1 uses the identity for \[ a^3+b^3. \]
\[ \boxed{(b)} \]