Question

Find a and b if-
9√3 +8√5 - (4√5 - 3√3) = a√3 + b√5

Answer 1

Answer :

$9 \sqrt{3} + 8 \sqrt{5} - (4 \sqrt{5} - 3 \sqrt{3} ) = a \sqrt{3} + b \sqrt{5} \\ \\ to \: find \: the \: value \: of \: a \: \: and \ \: b \: \\ \\ we \: will \: solve \: left \: hand \: side \\ \\ l.h.s \: = > \\ \\9 \sqrt{3} + 8 \sqrt{5} - (4 \sqrt{5} - 3 \sqrt{3} ) \\ \\ firstly \: solve \: bracket \\ \\ = > \: 9 \sqrt{3} + 8 \sqrt{5} - 4 \sqrt{5} + 3 \sqrt{3} \\ \\ collect \: like \: terms \\ \\ (9 + 3) \sqrt{3} + (8 - 4) \sqrt{5} \\ \\ 12 \sqrt{3} + 4 \sqrt{5}$
$so \: by \: solving \: l.h.s \\ \\ we \: get \: \\ \\ a \: = 12 \\ \\ b = 4$

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