Question:
If x = 3y + 4, then what is the value of $(x^3 – 27y^3 – 36 xy)$?
यदि x = 3y + 4 है, तो $(x^3 – 27y^3 – 36 xy)$ का मान क्या है?
Options:
- a) 8
- b) 1
- c) 64
- d) 27
- a) 8
- b) 1
- c) 64
- d) 27
correct answer : c)
Explanation:
Given: $x = 3y + 4 \implies x – 3y = 4$.
We cubing both sides:
$(x – 3y)^3 = 4^3$
$\implies x^3 – (3y)^3 – 3 \times x \times (3y)(x – 3y) = 64$
$\implies x^3 – 27y^3 – 9xy(x – 3y) = 64$
Substitute $x – 3y = 4$:
$\implies x^3 – 27y^3 – 9xy(4) = 64$
$\implies x^3 – 27y^3 – 36xy = 64$.
Hence, option (c) is the correct answer.
दिया गया है: $x = 3y + 4 \implies x – 3y = 4$।
दोनों पक्षों का घन (cube) करने पर:
$(x – 3y)^3 = 4^3$
$\implies x^3 – (3y)^3 – 3 \times x \times (3y)(x – 3y) = 64$
$\implies x^3 – 27y^3 – 9xy(x – 3y) = 64$
$x – 3y = 4$ प्रतिस्थापित करें:
$\implies x^3 – 27y^3 – 9xy(4) = 64$
$\implies x^3 – 27y^3 – 36xy = 64$।
अतः, विकल्प (c) सही उत्तर है।