Find the value of x^2 + y^2 from the system of quadratic equations
If the system of quadratic equations is
x² = 17x + y
y² = x + 17y
x ≠ y
Then find the value of x² + y² =?
Solution
Let
x² = 17x + y …………….eq(1)
y² = x + 17y …………….eq(2)
Add equation 1 and equation 2, then
x² + y² = 17x + y + (x + 17y)
⇒ x² + y² = 18x + 18y
⇒ x² + y² = 18(x + y) ……….eq(3)
Now we need to find x + y to find the value of x² + y²
To find “x + y” subtract equation 2 and equation 1
Thus, x² – y² = 17x + y – (x + 17y)
⇒ x² – y² = 16x – 16y
⇒ (x + y)(x – y) = 16(x – y)
divide with x – y (we know x ≠ y so x – y ≠ 0)
⇒ x + y = 16 …………..eq(4)
From equation 3 and equation 4
x² + y² = 18(x + y)
⇒ x² + y² = 18 × 16
⇒ x² + y² = 288
