Question

the square root of x square y square + Y square by 4 x square minus x by Y + y by 2 x minus 3 by 4 is ​

Answer 1

Step-by-step explanation:

Given the square root of x square / y square + Y square by 4 x square minus x by Y + y by 2 x minus 3 by 4 is  

• We have the equation as  
• So √x^2/y^2 + y^2/4x^2 – x/y + y/2x – ¾
• So taking LCM we get
• √4x^4 + y^4 – 4x^3y + 2xy^3 – 3x^2y^2 / 4x^2y^2
• Now rearranging the x and y terms we get
• √4x^4 – 4x^3y – 3x^2y^2 + 2xy^3 + y^4 / 4x^2y^2
• Now taking the square root we get √(2x^2 – xy – y^2)^2 / 4x^2y^2
•             So we get 2x^2 – xy – y^2 / 2x^2y^2
• We can write this as x/y – 1/2 – y/2x
•                       OR  
•    √(x/y)^2 + (y/2x)^2 – x/y + y/2x – ¾ + 1 – 1 (add and subtract 1 to both sides)
•  √(x/y)^2 + (y/2x)^2 – 1 – x/y + y/2x + 1/4  
•      Let P = √(x/y)^2 + (y/2x)^2 – 2(x/y)(y/2x) – x/y + y/2x + ¼
•      Squaring both sides we get
•     So p^2 = (x/y – y/2x)^2 – (x/y – y/2x – 1/4)
•       Now let x/y – y/2x = a
•  So p^2 = a^2 – (a – 1/4 )
•     Or p^2 = a^2 – (4a – 1 / 4)
•     Or p^2 = 4a^2 – 4a + 1 / 4
•      P^2 = (2a – 1 / 2)^2
• Or p = 2a – 1 / 2
•       Or p = a – 1/2  
•      Or p = x/y – y/2x – 1/2  

Reference link will be

https://brainly.in/question/18440895

https://brainly.in/question/11308751