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प्रश्न
Find the value of a and b if `(sqrt(7) - 2)/(sqrt(7) + 2) = asqrt(7) + b`.
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उत्तर
`(sqrt(7) - 2)/(sqrt(7) + 2) = asqrt(7) + b`
⇒ `((sqrt(7) - 2)(sqrt(7) - 2))/((sqrt(7) + 2)(sqrt(7) - 2)) = asqrt(7) + b`
⇒ `(sqrt(7) - 2)^2/((sqrt(7))^2 - 2^2) = asqrt(7) + b`
`((sqrt(7))^2 - 2(sqrt(7))(2) + 2^2)/(7 - 4) = asqrt(7) + b`
`(7 - 4sqrt(7) + 4)/3 = asqrt(7) + b`
`(11 - 4sqrt(7))/3 = asqrt(7) + b`
`11/3 + (-4 sqrt(7))/3 = asqrt(7) + b`
`acancel(sqrt(7)) = (-4 cancel(sqrt(7)))/3`
∴ a = `(- 4)/3`
`11/3 + (-4)/3 = a + b`
∴ a = `(- 4)/3 and b = 11/3`
∴ The value of a = `(- 4)/3 and b = 11/3`
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