If $a : b = 2 : 3$, then find the value of $(7a^3 – 2b^3) : (b^3 – a^3)$.
If $a : b = 2 : 3$, then find the value of $(7a^3 – 2b^3) : (b^3 – a^3)$.
यदि a : b = 2 : 3 है, तो $(7a^3 – 2b^3) : (b^3 – a^3)$ का मान ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
2 : 19
Given:
a : b = 2 : 3
Let,
$a = 2x,; b = 3x$
Now substitute in the expression:
$\frac{7a^3 - 2b^3}{b^3 - a^3}$
$a^3 = (2x)^3 = 8x^3$
$b^3 = (3x)^3 = 27x^3$
Substitute:
$\frac{7(8x^3)-2(27x^3)}{27x^3-8x^3}$
$= \frac{56x^3-54x^3}{19x^3}$
$= \frac{2x^3}{19x^3}$
$= \frac{2}{19}$
Final Answer: 2:19
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