Question

If 20 + 6root (5 )= a +2root (b), then find the values of a and b. (a, b = Q)
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Answer 1

Answer:

a=20 and b = 45

explanation:

20 + 6root5 = a + 2rootb

$20 + 6 \sqrt{5} = a + 2 \sqrt{b} \\ we \: know \: that \\ simple \: a \: is \: related \: to \: 20 \\ so \\ \: a = 20 \\ and \: we \: knw \: that \: 2 \sqrt{b} \: is \: related \: to \: 6 \sqrt{5} \\ then \\ outside \: f \: root \: is2 \: in \: (2 \sqrt{b} ) \\ so \: we \: take \: only \: 2 \: outside \: of \: 6 \sqrt{5} \: also \\ then \\ 6 \sqrt{5} = 2 \sqrt{3 \times 3 \times 5} = 2 \sqrt{45} \\ and \\ 2 \sqrt{45} = 2 \sqrt{b} \\ hence \\ b \: = \: 45 \\ \\ a = 20 \: \: and \: b \: = \: 45$