If ax + by = 1 and bx + ay = 2abovera²+b² then the value of x (in terms of a and b) is:

If ax + by = 1 and bx + ay = 2abovera²+b² then the value…

If ax + by = 1 and bx + ay = $2ab\over{a^2+b^2}$ then the value of x (in terms of a and b) is:

Show answer & explanation

Correct answer: B

Explanation

The correct answer is option 2 i.e. $a\over{a^2+b^2}$ .

ax + by = 1

⇒ a²x + aby = a .....(1)

bx + ay = $2ab\over{a^2+b^2}$

⇒ b²x + aby = $2ab^2\over{a^2+b^2}$ .....(2)

Subtract equation (2) from (1),

(a²x - b²x) = a - $2ab^2\over{a^2+b^2}$

⇒ x(a² - b²) = $\frac{[a(a^2 + b^2) - 2ab^2]}{(a^2 + b^2) }$ = $\frac{(a^3 + ab^2 - 2ab^2)}{(a^2 + b^2)}$

⇒ x(a² - b²) = $\frac{a(a^2 - b^2)}{(a^2 + b^2)}$

⇒ x = $a\over{a^2+b^2}$