Question

(1-x²-y²) from (xy+y²-x²+1)​

Answer 1

Answer:

do it like that

Step-by-step explanation:

(x² + x × y + y²) = 1………………. (1)

Suppose that, x & y are real numbers; therefore :

(x - y)² ≥ 0 and both x², y² ≥ 0

Or, (x² - 2×x×y + y²) ≥ 0 ………………….. (2)

Multiplying equation (1) by 2 and in equation (2), we get

2×(x²+ x×y + y²) + (x² - 2×x×y + y²) ≥ 2×1 + 0

or, 2×x²+ 2×x×y + 2×y² + x² - 2×x×y + y² ≥ 2

or, 3×x² + 3×y² ≥ 2

or, 3×(x²+ y²) ≥ 2

or, (x²+ y²) ≥ (2 / 3) ………………………….. (3)

Taking square root on both sides, we get

√(x²+ y²) ≥ √(2 / 3)

Therefore, √(x²+ y²) = √(2 / 3)