Question

plzz solve this question step by step fast i will mark you brainlist

Answer 1

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Answer 2

Let (1/x + y) = u and (1/x - y) = v.

Given Equation is 10u + 20v = 200   ----- (1)

Given Equation is 20u - 10v = 100     ------ (2)

On Adding (1) & (2), we get

⇒ 10u + 20v + 20u - 10v = 200 + 100

⇒ 30u + 10v = 300     ------ (3)

On subtracting (1) & (2), we get

⇒ 10u + 20v - 20u + 10v = 200 - 100

⇒ -10u + 30v = 100    ------ (4)

On solving (3) & (4) * 3, we get

⇒ 30u + 10v = 300

⇒ -30u + 90v = 300

   -------------------------

               100v = 600

                    v = 6.

⇒ (1/x - y) = 6.    

⇒ 6(x - y) = 1

⇒ 6x - 6y = 1  ------ (5)

Substitute v = 6 in (3), we get

⇒ 30u + 10v = 300

⇒ 30u + 10(6) = 300

⇒ 30u + 60 = 300

⇒ 30u = 240

⇒ u = 8.

⇒ (1/x + y) = 8    

⇒ 8(x + y) = 1

⇒ 8x + 8y = 1 ------- (6)

On adding (5) & (6), we get

⇒ 6x - 6y + 8x + 8y = 1 + 1

⇒ 14x + 2y = 2    ----- (7)

On subtracting (5) & (6), we get

⇒ 6x - 6y - 8x - 8y = 0

⇒ -2x - 14y = 0    ------- (8)

On solving (7) & (8) * 7, we get

⇒ 14x + 2y = 2

⇒ -14x - 98y = 0

   ---------------------

             -96y = 2

                  y = -1/48.

Substitute y = -1/48 in (7), we get

⇒ 14x + 2y = 2

⇒ 14x + 2(-1/48) = 2

⇒ 14x - 1/24 = 2

⇒ 14x = 49/24

⇒ x = 7/48.

Therefore, the value of x = 7/48 and y = -1/48.

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