Question

Solve:-
$(2x + 3)^{2} \: + \: (2x + 3)^{2} \: = \: (8x + 6) \: (x - 1) \: + 22$
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Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

Solve:-

$(2x + 3)^{2} \: + \: (2x + 3)^{2} \: = \: (8x + 6) \: (x - 1) \: + 22$

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$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

Use ( a + b )² + ( a - b )² = 2(a + b )² on LHS

${:}\longrightarrow \sf{(2x + 3)^{2} \: + \: (2x + 3)^{2} \: = \: (8x + 6) \: (x - 1) \: + 22 }$

${:} \longrightarrow \sf{\sf{2( {2x}^{2} \: + \: {3}^{2}) \: = \: x(8x + 6) \: - (8x + 6) \: + \: 22 }}$

${:} \longrightarrow \sf{\sf{2( {4x} \: + \: {9}) \: = \: 8 {x}^{2} + 6x\: - \: 8x + 6 \: + \: 22 }}$

${:} \longrightarrow \sf{\sf{8 {x}^{2} \: + 18 \: = \: 8 {x}^{2} - 2x \: + 16 }}$

${:} \longrightarrow \sf{\sf{8 {x}^{2} \: - \: 8 {x}^{2} \: + 2x \: = \: 16 \: - \: 18 }}$

${:} \longrightarrow \sf{\sf{2x \: = \: - 2 }}$

${:} \longrightarrow \sf{\sf{x \: = \: \cancel \frac{ - 2}{2} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: -1 }}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Solution \: of \: given \: equation \: = \underline {\underline{ -1}}}\\\end{gathered}\end{gathered}$

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More to know:-

Some Important Algebraic Identities:-

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{minipage}}$

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Answer 2

Answer:

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$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}} </p><p>✠Solution:−</p><p> </p><p> </p><p> </p><p> </p><p></p><p>Use ( a + b )² + ( a - b )² = 2(a + b )² on LHS</p><p>\begin{gathered} \\ \\ \\ \end{gathered}$

Step-by-step explanation:

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