Find the value of a and b if ( 2 - √7 ) ÷( 2 + 3√7 ) = a + b√7. Please tell with explanation.
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Step-by-step explanation:
(2-√7) /2+3√7) × (2-3√7) / (2-3√7)
(2-√7) (2+3√7) / 4 - 63
[multiply by conjugate of the numerator ie by
2-3√7 ]
=> (4+6√7-2√7-21) / -59
=> (-17 + 4√7) / -59
=> 17/59 - 4/59 √7
[ compare this with given RHS a+b√7 ]
on comparing we get a = 17/59 and b = - 4/59
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