Math, asked by Sajidmahammad56, 5 hours ago

22/x+y+15/x-y=5,55/x+y +40/x-y=13​

Answers

Answered by RvChaudharY50
2

Question :- Solve :- 22/x+y+15/x-y=5,55/x+y +40/x-y=13

Solution :-

given that,

22/x+y + 15/x-y = 5

55/x+y + 40/x-y = 13

Let ,

  • 1/x + y = a
  • 1/x - y = b

so,

→ 22a + 15b = 5 -------- Eqn.(1)

→ 55a + 40b = 13 --------- Eqn.(2)

multiply Eqn.(1) by 5 and Eqn.(2) by 2 and then subtracting the result from Eqn.(2) result ,

→ 2(55a + 40b) - 5(22a + 15b) = 2 * 13 - 5 * 5

→ 110a - 110a + 80b - 75b = 26 - 25

→ 5b = 1

→ b = (1/5)

putting value of b in Eqn.(1)

→ 22a + 15(1/5) = 5

→ 22a = 5 - 3

→ a = 2/22

→ a = (1/11)

then,

→ (1/x + y) = a

→ (1/x + y) = 1/11

→ x + y = 11 -------- Eqn.(3)

and,

→ (1/x - y) = b

→ (1/x - y) = 1/5

→ x - y = 5 -------- Eqn.(4)

adding Eqn.(3) and Eqn.(4) now,

→ x + y + x - y = 11 + 5

→ 2x = 16

→ x = 8 (Ans.)

putting value of x in Eqn.(4)

→ 8 - y = 5

→ y = 8 - 5

→ y = 3 (Ans.)

Hence, value of x is 8 and value of y is 3 .

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if a²+ab+b²=25

b²+bc+c²=49

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Answered by hukam0685
2

Step-by-step explanation:

Given:

 \frac{22}{x + y}  +  \frac{15}{x - y}  = 5 \\  \\  \frac{55}{x + y}  +  \frac{40}{x - y}  = 13 \\

To find: Find the value of x and y

Solution:

Tip: Convert given equations in standard linear equations

Step 1: Let

 \frac{1}{x + y}  = a...eq1 \\  \\  \frac{1}{x - y}  = b...eq2 \\  \\

Substitute these in given equations

22a + 15b = 5 ...eq3\\  \\ 55a + 40b = 13...eq4 \\

Step 2: Solve eq3 and eq4 for a and b

Multiply eq3 by 5 and eq4 by 2 and subtract both

110a + 75b = 25 \\ 110a + 80b = 26 \\  (-)  \:  \:  \:  \:  (-)  \:  \:  \:  \:  \:  \:  \: ( -)  \\  -  -  -  -  -  -  -  \\  - 5b =  - 1 \\  \\ \bold{\pink{b =  \frac{  1}{5}}}  \\

put the value of b in eq3

22a + 15 \times  \frac{1}{5}  = 5 \\  \\ 22a + 3 = 5 \\  \\ 22a = 2 \\  \\ \bold{\purple{a =  \frac{1}{11}}}  \\  \\

Step 3: Put the value of a and b in eq 1 and eq2

 \frac{1}{x  +  y}  =  \frac{1}{11}  \\ \\ or \\   \\ x + y = 11...eq5 \\  \\ \frac{1}{x - y}   =  \frac{1}{5}  \\  \\ or \\  \\ x - y = 5 \: ...eq6 \\

Step 4: Add eq5 and eq 6 to find value of x and y

x + y = 11 \\ x - y = 5 \\  -  -  -  -  -  \\ 2x = 16 \\  \\ x =  \frac{16}{2}  \\  \\ x = 8 \\  \\

put the value of x in eq5

8 + y = 11 \\  \\ y = 11 - 8 \\  \\ y = 3 \\  \\

Final answer:

\bold{\red{x = 8}}\\  \\\bold{\green{ y = 3}} \\  \\

Verification:

Put value if x and y in eq

 \frac{22}{x + y}  +  \frac{15}{x - y}  = 5 \\ \\\frac{22}{8+3}  +  \frac{15}{8-3}  = 5\\\\\frac{22}{11}  +  \frac{15}{5}  = 5\\\\2+3  = 5\\\\5=5\\\\

Hope it helps you.

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