Find the value of a and b 3+2✓2/3-✓2=2a+b✓2/3
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We need to rationalize the denominator
Rationalising factor = 3+√2
= 3+2√2/3-√2
= (3+2√2)/(3-√2) × (3+√2)/(3+√2)
= [(3+2√2)(3+√2)]/[(3-√2)(3+√2)]
= (9+3√2+6√2+2(2))/(3²-√2²)
= (9+9√2+4)/(9-2)
= (13+9√2)/7
= 13/7 + 9√2/7
= 2(13/14) + (27/7)(√2/3)
= 2a + b√2/3
By comparing, we get
a = 13/14 and b = 27/7
Hope it helps
Rationalising factor = 3+√2
= 3+2√2/3-√2
= (3+2√2)/(3-√2) × (3+√2)/(3+√2)
= [(3+2√2)(3+√2)]/[(3-√2)(3+√2)]
= (9+3√2+6√2+2(2))/(3²-√2²)
= (9+9√2+4)/(9-2)
= (13+9√2)/7
= 13/7 + 9√2/7
= 2(13/14) + (27/7)(√2/3)
= 2a + b√2/3
By comparing, we get
a = 13/14 and b = 27/7
Hope it helps
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