Question

x^3 – 8y^3 – 36xy – 216, when x = 2y + 6, find the value of

Answer 1

Answer :

$\large{\star\:\:\boxed{\bf{x\:=\:0\:\:\:and\:\:\:y\:=\:(-3)}}\:\:\star}$

Complete Question :–

x³ – 8y³ – 36xy – 216 , when x = 2y + 6, find the value of x and y .

Explanation :

Given :–

• x³ - 8y³ - 36xy is a Polynomial .
• x = 2y + 6 is a solution of x³ – 8y³ – 36xy – 216 .

To Find :–

The Values of x and y .

Formula Applied :–

• $\boxed{\star\:\:\bf{(a\:+\:b)^3\:=\:a^3\:+\:b^3\:+3a^{2}b\:+\:3ab^{2}}\:\:\star}$

Solution :–

We have x = 2y + 6 ------------(1)

Putting this value of 'x' in Equation(1) :-

$\rightarrow\sf{x^3 \:-\: 8y^3 \:- \:36xy\: -\: 216\:=\:0}$

$\rightarrow\sf{(2y\:+\:6)^3 \:-\: 8y^3 \:- \:3(2y\:+\:6)y\: -\: 216\:=\:0}$

$\rightarrow\sf{8y^3\:+\:216\:+\:3(2y)^2(6)\:+\:3(2y)(6)^2 \:-\: 8y^3 \:- \:3(2y\:+\:6)y\: -\: 216\:=\:0}$

$\rightarrow\sf{8y^3\:+\:216\:+\:3(4y^2)(6)\:+\:3(2y)(36) \:-\: 8y^3 \:- \:3(2y\:+\:6)y\: -\: 216\:=\:0}$

$\rightarrow\sf{8y^3\:+\:216\:+\:72y^2\:+\:216y \:-\: 8y^3 \:- \:6y^2\:-\:18y\: -\: 216\:=\:0}$

$\rightarrow\sf{72y^2\:+\:216y \:-\:6y^2\:-\:18y\:=\:0}$

$\rightarrow\sf{66y^2\:+\:198y\:=\:0}$

$\rightarrow\sf{66y^2\:=\:(-198y)}$

$\rightarrow\sf{66y\:=\:(-198)}$

$\rightarrow\sf{y\:=\:\left(-\dfrac{198}{66}\right)}$

$\rightarrow\boxed{\bf{y\:=\:(-3)}}$

Now , Putting this Value of 'y' in Equation(2) :-

$\rightarrow\sf{x\:=\:2y\:+\:6}$

$\rightarrow\sf{x\:=\:2(-3)\:+\:6}$

$\rightarrow\sf{x\:=\:(-6)\:+\:6}$

$\rightarrow\sf{x\:=\:0}$

∴ The value of x is 0 and y is (-3) .

Answer 2

✪ᴀɴsᴡᴇʀ✪

• $\boxed{ x^3 - 8y^3 - 36xy - 216 = 0}$

★ɢɪᴠᴇɴ★

• A polynomial $x^3 – 8y^3 – 36xy – 216$

• $x = 2y + 6$

☆ᴛᴏ ғɪɴᴅ☆

• Value of $x^3 – 8y^3 – 36xy – 216$

✫ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ✫

Here,

$\to x = 2y + 6$

$\to x - 2y = 6$

$\to (x - 2y)^3 = 6^3$

$\to x^3 - (2y)^3 - 3x.2y(x - 2y) = 216$

$\to x^3 - 8y^3 - 6xy(6) = 216$

$\to x^3 - 8y^3 - 36xy = 216$

$\to x^3 - 8y^3 - 36xy - 216 = 0$