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प्रश्न
Solve for x and y:
`sqrt(2)x + sqrt(3)y = 5` and `sqrt(3)x + sqrt(8)y = -sqrt(6)`
योग
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उत्तर
Given: `sqrt(2)x + sqrt(3)y = 5` and `sqrt(3)x + sqrt(8)y = -sqrt(6)`.
Using Cramer’s rule (cross-multiplication for 2 × 2 systems).
Let `a = sqrt(2), b = sqrt(3), c = sqrt(3), d = sqrt(8) = 2sqrt(2)`
RHS e = 5, f = `-sqrt(6)`
Compute the determinant D = ad – bc
= `sqrt(2) xx (2 sqrt(2)) - sqrt(3) xx sqrt(3)`
= 2 × 2 – 3
= 4 – 3
= 1
`x = (ed - bf)/D`
= `(5 xx (2 sqrt(2)) - sqrt(3) xx (-sqrt(6)))/1`
= `10sqrt(2) + sqrt(18)`
= `10sqrt(2) + 3sqrt(2)`
= `13sqrt(2)`
`y = (af - ec)/D`
= `(sqrt(2)(-sqrt(6)) - 5sqrt(3))/1`
= `-sqrt(12) - 5sqrt(3)`
= `-2sqrt(3) - 5sqrt(3)`
= `-7sqrt(3)`
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