Question

ʜᴇʟʟᴏ

ᴍᴀᴛʜꜱ
ᴄʟᴀꜱꜱ 10
ᴄʜ - qᴜᴀᴅʀᴀᴛɪᴄ ᴇqᴜᴀᴛɪᴏɴꜱ
•ᴩʟᴇᴀꜱᴇ ᴀɴꜱᴡᴇʀ ᴛʜᴇ qᴜᴇꜱᴛɪᴏɴ.
•ᴩʟᴇᴀꜱᴇ ᴀɴꜱᴡᴇʀ ᴀʟʟ ᴛʜᴇ ᴩᴀʀᴛꜱ ᴏꜰ qᴜᴇꜱᴛɪᴏɴ.

ᴛʜᴀɴᴋꜱ​​

Answer 1

Step-by-step explanation:

Given:-

★ If the roots of the equation (a²+ b²) x² - 2 (ac + bd) x + (c² + d²) = 0.

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Find:-

★ Prove that it's equal to (a/b = c/d) .

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Calculations:-

Here, D is equal to (b² -4ac = 0).

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Moving on to further calculations to prove:

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⇢ $\sf{\bigg(2(ab + cd)\bigg)^{2} - 4(a^{2} + b^{2}) (c^{2} + d^{2}) = 0}$

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⇢ $\sf{4(ab+ cd)^{2} - 4(a^{2} + b^{2}) (c^{2} + d^{2}) =0}$

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Now adding separate brackets:ㅤ

$\sf{\bigg(a^{2} b^{2} + c^{2} d^{2} + 2abcd\bigg) - a^{2} c^{2} - a^{2} d^{2} - b^{2} d^{2} - b^{2} c^{2} = 0}$

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⇢ $\sf{-a^{2} c^{2} \pm b^{2} d^{2} \pm 2abcd = 0}$

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⇢ $\sf{\bigg((ac - bd)^{2}\bigg) = 0}$

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Now, remove the brackets and simplify:

⇢$\sf{ac - bd = 0}$

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⇢ $\sf{ac = bd}$

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⇢${\boxed{\bold{a/b = d/c}}}$

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⇢ LHS = RHS

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HENCE PROVED!!!

Answer 2

Hello Dear!

Here's your Answer!

Kindly refer to the attachment for answer!