Question

Solve it :-


( x-4 ) (x-6 ) = ( x-2 ) (x-4 )​

Answer 1

Answer:

(−+4)(−6)=(−2)(−4)

{\color{#c92786}{(-x+4)(x-6)}}=(x-2)(x-4)(−x+4)(x−6)=(x−2)(x−4)

−1⋅(−6)+4(−6)=(−2)(−4)

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Answer 2

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

• $( \: x - 4 \: ) \: (x - 6) \: = \: (x - 2) \: (x - 4)$

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

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: ( \: x - 4 \: ) \: (x - 6) \: = \: (x - 2) \: (x - 4) }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

Multiple the Terms.

$\qquad \quad {:} \longrightarrow \sf{\sf{ x (x - 6) \: - 4(x - 6) \: = \: x (x - 4) \: - 2(x - 4) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ {x}^{2} - 6x \: - 4x + 24 \: = \: {x}^{2} - 4x\: - 2x + 8 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \cancel\red { {x}^{2} } - 6x \: - 4x + 24 \: = \: \cancel\red { {x}^{2} } - 4x\: - 2x + 8 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ -10x + 24 \: = \: - 6x + 8 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ -10x \: + \:6x \: = \: 8 \: - \: 24 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ -4x\: = \: - 16}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ x\: = \: \cancel \green{ \frac{ \red- 16}{ \red- 4} }}}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: 4 }}}$

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

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: ( \: x - 4 \: ) \: (x - 6) \: = \: (x - 2) \: (x - 4) }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

Putting the Value Of x

$\qquad \quad {:} \longrightarrow \sf{\sf{ ( \: 4- 4 \: ) \: (4 - 6) \: = \: (4- 2) \: (4 - 4) }}$

Multiple them, as we have done earlier

$\qquad \quad {:} \longrightarrow \sf{\sf{ 4(4 - 6) \: - 4(4 - 6) \: = \: 4(4- 4) \: - 2(4 - 4) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 4(4 - 6) \: - 4(4 - 6) \: = \: 4(4- 4) \: - 2(4 - 4) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 16 - 24 \: - 16 + 24 \: = \: 16 - 16 \: - 8 + 8 }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \cancel \red{16} \: \cancel \green{ - 24}\: \cancel \red{ - 16} \: \cancel \green{ + 24} \: = \: \cancel \purple{16} \: \cancel \purple{ - 16} \:\cancel \pink{ - 8} \: \cancel \pink{ + 8} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{0 \: = \: 0}}}$

Hence, Proved

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ x \: = \underline {\underline{ 4}}}\\\end{gathered}\end{gathered}$

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