Question

Solve for X and Y Mx + ny = m+nm( 1/m-n - 1/m+n)X + n(1/n-m - 1/m+n)y = 2m/m+n

Answer 1

mx + ny = m + n ----(1)

m{1/(m - n) - 1/(m + n)}x + n{1/(n - m) - 1/(m + n)y = 2m/(m + n)
⇒m{(m + n - m + n)/(m² - n²)}x + n{(m + n - n + m)/(n² - m²)}y = 2m/(m+n)
⇒2mn/(m² -n²)x + 2mn/(n²-m²)y = 2m/(m+n)
⇒2mn/(m²-n²) - 2mn/(m²-n²)y = 2m/(m+n)
⇒2m/(m+n)[nx/(m-n)-ny/(m - n)] = 2m/(m+n)
⇒nx - ny = (m - n) --------(2)

Now, solve equations (1) and (2)
x(m + n) = 2m ⇒ x = 2m/(m + n) , put it in equation (1)
ny = m + n - 2m²/(m + n) =( n²+2mn-m²)/(m+n)
y = (n²+2mn-m²)/(mn + n²)

Answer 2

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