Question

maths assignment
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Answer 1

Step-by-step explanation:

hope it will help you. good luck

Answer 2

Solution :

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(1)

$\longrightarrow \sf If \: \: m = x + \frac{1}{x} \: \: and \: \: n = x - \frac{1}{x}$

Then, m² - n² = (?)

$\longrightarrow \sf m² - n²$

$\longrightarrow \sf \bigg( x + \frac{ 1}{x}\bigg)^{2} - \bigg(x - \frac{1}{x}\bigg)^{2}$

$\longrightarrow \sf \bigg( x + \frac{1}{x}+ \bigg(x - \frac{1}{x} \bigg)\bigg) \bigg( x + \frac{1}{x} - \bigg( x - \frac{1}{x} \bigg) \bigg)$

$\longrightarrow \sf \bigg( x + \cancel{ \frac{1}{x}} + \bigg(x \cancel{ - \frac{1}{x}} \bigg)\bigg) \bigg( x + \frac{1}{x} - x + \frac{1}{x} \bigg)$

$\longrightarrow \sf \bigg( x + x \bigg) \bigg( \cancel{x } + \frac{2}{x} \cancel{ - x } \bigg)$

$\longrightarrow \sf ( 2x) ( \frac{2}{x} )$

$\longrightarrow \sf (2 \cancel{x}) ( \frac{2}{\cancel{x}} )$

$\longrightarrow \sf 2 × 2$

$\longrightarrow \sf \underline{\fbox{4}}$

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(2)

$\longrightarrow \sf x² - x - 12$

$\longrightarrow \sf x² + 3x - 4x - 12$

$\longrightarrow \sf x ( x + 3) - 4(x + 3)$

$\longrightarrow \sf \underline{ \fbox{(x + 3) (x -4)} }$

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(3)

$\longrightarrow \sf 6x² + 5x - 6$

$\longrightarrow \sf 6x² + 9x - 4x - 6$

$\longrightarrow \sf 3x(2x + 3) - 2(2x + 3)$

$\longrightarrow \sf \underline{ \fbox{(2x + 3) (3x - 2) }}$

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I hope it helps you ❤️✔️