Math, asked by ikannu4955, 8 months ago

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

Answers

Answered by atahrv
28

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) .

Answered by saounksh
4

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

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