二次根式因式分解在实数范围内分解因式：2x²y²-5xy+1

Question

二次根式因式分解
在实数范围内分解因式：2x²y²-5xy+1

Answer 1

：2x²y²-5xy+1
=2[(xy)²-5xy/2]+1
=2[(xy)²-5xy/2+25/16]+1-2×25/16
=2(xy-5/4)²-17/8
=2(xy-5/4)²-√(17/8)²
=[√2(xy-5/4)]²-(√34/4)²
=(√2xy-5√2/4+√34/4)(√2xy-5√2/4-√34/4)
=[√2xy-(5√2-√34)/4][√2xy-(5√2+√34)/4]