Question

anyone please solve these problems​

Answer 1

Step-by-step explanation:

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$\red{\bold{\underline{\underline{❥Question᎓}}}} </p><p>$❥Question᎓

Q:-Find the value of

$\sqrt{a - b}$

a−b

if

$\frac{8 + 3 \sqrt{7} }{8 - 3 \sqrt{7} } - \frac{8 - 3 \sqrt{7} }{8 + 3 \sqrt{7} } = a + b \sqrt{7}$

$\huge\tt\underline\blue{⛶Answer⛶ }$

⛶Answer⛶

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⟹$\bold{ \frac{8 + 3 \sqrt{7} }{8 - 3 \sqrt{7} } - \frac{8 - 3 \sqrt{7} }{8 + 3 \sqrt{7} } = a + b \sqrt{7}}$⟹

⟹$\bold{ \frac{(8 + 3 \sqrt{7})(8 + 3 \sqrt{7}) - [(8 - 3 \sqrt{7} )(8 - 3 \sqrt{7}) ]}{(8 + 3 \sqrt{7} )(8 - 3 \sqrt{7} )}}$⟹

∵$\bold{ {(a + b)}^{2} - {(a - b)}^{2}$ =

⟹ $\bold{\frac{4 \times 8 \sqrt{7} }{ {(8)}^{2} - {(3 \sqrt{7}) }^{2} } = a + b \sqrt{7} }$⟹

⟹ $\bold{\frac{32 \sqrt{7} }{64 - 63} = a + b \sqrt{7}}$⟹

64−63

32

7

=a+b

7

⟹$\bold{ \frac{32 \sqrt{7} }{1} = a + b \sqrt{7}}$⟹

{7} = a + b \sqrt{7}}[/tex]⟹32

7

⟹$\bold{0 + 32 \sqrt{7} = a + b \sqrt{7} }$⟹0+32

$\bold{\red{On \:comparing\: both \:sides:-}}$Oncomparingbothsides:−

⟹$\bold{a = 0 \: and \: b = 32}$⟹a=0andb=32

⟹$\bold{now \: \sqrt{a - b} = \sqrt{0 - 32} = \sqrt{ - 32 } = \sqrt{ - 2 \times 16} = 4 \sqrt{ - 2} = 4 \sqrt{2} i \: [( {i}^{2} = - 1)}$⟹now

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Answer 2

Answer:

$⟹\bold{ \frac{8 + 3 \sqrt{7} }{8 - 3 \sqrt{7} } - \frac{8 - 3 \sqrt{7} }{8 + 3 \sqrt{7} } = a + b \sqrt{7}}8−378+37−8+378−37=a+b7 ⟹</p><p></p><p>⟹\bold{ \frac{(8 + 3 \sqrt{7})(8 + 3 \sqrt{7}) - [(8 - 3 \sqrt{7} )(8 - 3 \sqrt{7}) ]}{(8 + 3 \sqrt{7} )(8 - 3 \sqrt{7} )}}(8+37)(8−37)(8+37)(8+37)−[(8−37)(8−37)] ⟹</p><p></p><p>∵\bold{ {(a + b)}^{2} - {(a - b)}^{2} =</p><p></p><p>⟹ \bold{\frac{4 \times 8 \sqrt{7} }{ {(8)}^{2} - {(3 \sqrt{7}) }^{2} } = a + b \sqrt{7} }(8)2−(37)24×87=a+b7 ⟹</p><p></p><p>⟹ \bold{\frac{32 \sqrt{7} }{64 - 63} = a + b \sqrt{7}}64−63327=a+b7 ⟹</p><p></p><p>64−63</p><p></p><p>32</p><p></p><p>7</p><p></p><p>=a+b</p><p></p><p>7</p><p></p><p>⟹\bold{ \frac{32 \sqrt{7} }{1} = a + b \sqrt{7}}1327=a+b7 ⟹</p><p></p><p>{7} = a + b \sqrt{7}}$⟹32

7

⟹\bold{0 + 32 \sqrt{7} = a + b \sqrt{7} }0+327=a+b7 ⟹0+32

\bold{\red{On \:comparing\: both \:sides:-}}Oncomparingbothsides:− Oncomparingbothsides:−

⟹\bold{a = 0 \: and \: b = 32}a=0andb=32 ⟹a=0andb=32

⟹\bold{now \: \sqrt{a - b} = \sqrt{0 - 32} = \sqrt{ - 32 } = \sqrt{ - 2 \times 16} = 4 \sqrt{ - 2} = 4 \sqrt{2} i \: [( {i}^{2} = - 1)}nowa−b=0−32=−32=−2×16=4−2

[/tex]