Question

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Answer 1

Required Answer :

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Question 1

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Show that :

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ㅤㅤㅤ$\boxed{\sf{\red{ \dfrac{x^{a+b} \times x^{b+c} \times x^{c+a} }{ ( x^{a} \times x^{b} \times x^{c} ) } \:=\: 1 }}}$

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Applicable concept :

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( Law of exponents & power )

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Final Answer :

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ㅤ$\sf{ \implies \dfrac{ x^{a+b} \times x^{b+c} \times x^{a+c} }{ ( x^{a} \times x^{b} \times x^{c} )² }}$

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ㅤ$\sf{ \implies \dfrac{ x^{(a+b)+(b+c)} \times x^{a+c} }{ x^{2a} \times x^{2b} \times x^{2c} }}$

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ㅤ$\sf{ \implies \dfrac{x^{(a + 2b + c)+(a + c)} }{ x^{(2a + 2b + 2c)} } }$

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ㅤ$\sf{ \implies \dfrac{\cancel{ x^{(2a + 2b + 2c)}}^{\:\:\:\:1}}{ \cancel{ x^{(2a + 2b + 2c)}}}}$

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ㅤ$\sf{\implies \boxed{\sf{\green{1} \:=\: \green{R.H.S.}} }}$

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Question 2

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Solve the following equation :

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ㅤㅤㅤ$\boxed{\sf{\red{ \dfrac{ 5( 1 + x ) \:+\: 3( 1 + x ) }{ 1 - 2x } \:=\: 8 }}}$

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Applicable concept :

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( Simplification )

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ㅤ$\implies \sf{ \dfrac{ 5( 1 + x ) \:+\: 3( 1 + x ) }{ 1 - 2x } \:=\: 8 }$

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ㅤ$\implies \sf{ \dfrac{ ( 5 - 5x ) + ( 3 + 3x ) }{ 1 - 2x } \:=\: 8 }$

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ㅤ$\implies \sf{ \dfrac{ 5 + 3 - 5x + 3x }{ 1 - 2x } \:=\: 8 }$

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ㅤ$\implies \sf{ \dfrac{ 8 - 2x }{ 1 - 2x } \:=\: 8 }$

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ㅤ$\implies \sf{ 8 - 2x \:=\: 8 ( 1 - 2x ) }$

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ㅤ$\implies \sf{ 8 - 2x \:=\: 8 - 16x }$

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ㅤ$\implies \sf{ 8 - 16x \:=\: 8 - 2x }$

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ㅤ$\implies \sf{ -16x + 2x \:=\: 8 - 8 }$

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ㅤ$\implies \sf{ -14x \:=\: 0 }$

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ㅤ$\implies \sf{ x \:=\: \xcancel{\dfrac{0}{-16}} }$

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ㅤ$\implies \boxed{\sf{\green{ x \:=\: 0 }}}$

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ㅤㅤㅤ꧁ ʙʀᴀɪɴʟʏ×ᴋɪᴋɪ ꧂