Question

6+3√3 and 8-4√3 find the mean proportional between

Answer 1

Answer:

Step-by-step explanation

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Answer 2

$\large✠ \large{\textsf{\textbf { Question :}}}$

Find the mean proportional between 6 + 3√3 and 8 - 4√3.

$\large✠ \large{\textsf{\textbf { Answer :}}}$

$\sf\green{Let \: the \: mean \: proportion \: between \: 6 + 3 \sqrt{3} \: and \: 8 - 4 \sqrt{3} \: be \: x. }$

$\sf⟹ \bf\orange{6 + 3 \sqrt{3}, x \: and \: 8-4 \sqrt{3} \: are \: in \: continued \: proportion.}$

$\sf{⟹} \: \sf\pink{6 +3 \sqrt{3} : x =x : 8 - 4 \sqrt{3} }$

$\sf⟹ \: \sf\red{x \times x =(6 + 3 \sqrt{3} )(8 - 4 \sqrt{3}) }$

$\sf⟹ \: \sf\blue{ {x}^{2}=48+ 24 \sqrt{3} - 24 \sqrt{3} - 36}$

$\sf{⟹} \: \purple{ {x}^{2} = 12 }$

$\sf⟹ \sf{x = 2 \sqrt{3} }$

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$\tiny\bf {@MrAkdu}$