Question

if x+y=3 and x²+y²=5 then find the value of x and y​

Answer 1

Question:-

➡ If x + y = 3 and x² + y² = 5, then find the value of x and y.

Answer:-

➡The values of x and y are 2 and 1 or 1 and 2.

Solution:-

Given that,

➡ x + y = 3 .... (i)

➡ x² + y² = 5

Squaring both sides, we get,

➡ (x + y)² = 3²

➡ x² + y² + 2xy = 9

Substituting x² + y² here, we get,

➡ 5 + 2xy = 9

➡ 2xy = 9 - 5

➡ 2xy = 4

➡ xy= 2 (Remember this)

Now,

➡ x² + y² = 5

➡ x² + y² - 2xy = 5 - 2xy

➡ (x - y)² = 5 -(2×2)

➡ (x - y)² = 5 - 4

➡ (x - y)² = 1

➡ (x - y) = √1

➡ x - y = 1 (taking the positive value)

➡ x - y = 1 .... (ii)

Now, adding equations (i) and (ii), we get,

➡ x + y + x - y = 3 + 1

➡ 2x = 4

➡ x = 2

Now, we got x = 2

Substituting x in the equation (i), we get,

➡ x + y = 3

➡ 2 + y = 3

➡ y = 1

Now, we got y = 1.

Hence, the values of x and y are 2 and 1 respectively.

Formulae Used:-

➡ (x + y)² = x² + y² + 2xy

➡ (x - y)² = x² + y² - 2xy

Explanation:-

It's given that,

x +.y = 3 (i)

and,

x² + y² = 5

If we square equation 1,then we get x² + y² + 2xy = 9

As we know the value of x² + y², we have substituted it here.

So,

5 + 2xy = 9

➡ xy = 2

Now,

x² + y² = 5

If we subtract 2xy from both side, we get,

➡ x² + y² - 2xy = 5 - 4

As we know that, (x - y)² = x² + y² - 2xy

So,

(x-y)=√1 we get,

Now,

x + y=3

and

x - y = 1

Now, we can get the values of x and y by solving the simultaneous equation by elimination.

In this way, the problem is solved.

Answer 2

Answer:

Question:-

➡ If x + y = 3 and x² + y² = 5, then find the value of x and y.

Answer:-

➡The values of x and y are 2 and 1 or 1 and 2.

Solution:-

Given that,

➡ x + y = 3 .... (i)

➡ x² + y² = 5

Squaring both sides, we get,

➡ (x + y)² = 3²

➡ x² + y² + 2xy = 9

Substituting x² + y² here, we get,

➡ 5 + 2xy = 9

➡ 2xy = 9 - 5

➡ 2xy = 4

➡ xy= 2 (Remember this)

Now,

➡ x² + y² = 5

➡ x² + y² - 2xy = 5 - 2xy

➡ (x - y)² = 5 -(2×2)

➡ (x - y)² = 5 - 4

➡ (x - y)² = 1

➡ (x - y) = √1

➡ x - y = 1 (taking the positive value)

➡ x - y = 1 .... (ii)

Now, adding equations (i) and (ii), we get,

➡ x + y + x - y = 3 + 1

➡ 2x = 4

➡ x = 2

Now, we got x = 2

Substituting x in the equation (i), we get,

➡ x + y = 3

➡ 2 + y = 3

➡ y = 1

Now, we got y = 1.

Hence, the values of x and y are 2 and 1 respectively.

Formulae Used:-

➡ (x + y)² = x² + y² + 2xy

➡ (x - y)² = x² + y² - 2xy

Explanation:-

It's given that,

x +.y = 3 (i)

and,

x² + y² = 5

If we square equation 1,then we get x² + y² + 2xy = 9

As we know the value of x² + y², we have substituted it here.

So,

5 + 2xy = 9

➡ xy = 2

Now,

x² + y² = 5

If we subtract 2xy from both side, we get,

➡ x² + y² - 2xy = 5 - 4

As we know that, (x - y)² = x² + y² - 2xy

So,

(x-y)=√1 we get,

Now,

x + y=3

and

x - y = 1

Now, we can get the values of x and y by solving the simultaneous equation by elimination.

In this way, the problem is solved.