a, (2y -1)^3-2y(2y-3)^2-6y(2y-2) b, tìm x (2x+5)(2x-7)-(-4x-3)^2=16 (8x^2+3)(8x^2-3)-(8x^2-1)^2=22 01/10/2021 Bởi Elliana a, (2y -1)^3-2y(2y-3)^2-6y(2y-2) b, tìm x (2x+5)(2x-7)-(-4x-3)^2=16 (8x^2+3)(8x^2-3)-(8x^2-1)^2=22
a, \((2y -1)^3-2y(2y-3)^2-6y(2y-2)\) \(=8y^3-3.4y^2+3.2y-1-2y(4y^2-12y+9)-12y^2+12y\) \(=8y^3-12y^2+6y-1-8y^3+24y^2-18y-12y^2+12y\) \(=-1\) b,\((2x+5)(2x-7)-(-4x-3)^2=16\) \(\Leftrightarrow 4x^2-14x+10x-35-(16x^2+24x+9)=16\) \(\Leftrightarrow 4x^2-14x+10x-35-16x^2-24x-9=16\) \(\Leftrightarrow -12x^2-28x-60=0\) \(\Leftrightarrow -12(x^2+2.\dfrac{7}{6}x+\dfrac{49}{36})-\dfrac{131}{3}<0\) \(\forall x\) \(\Rightarrow \) pt vô nghiệm. \((8x^2+3)(8x^2-3)-(8x^2-1)^2=22\) \(\Leftrightarrow 64x^4-9-(64x^4-16x^2+1)=22\) \(\Leftrightarrow 16x^2=32\) \(\Leftrightarrow x^2=2\) \(\Leftrightarrow x=\pm\sqrt2\) Bình luận
a, \((2y -1)^3-2y(2y-3)^2-6y(2y-2)\)
\(=8y^3-3.4y^2+3.2y-1-2y(4y^2-12y+9)-12y^2+12y\)
\(=8y^3-12y^2+6y-1-8y^3+24y^2-18y-12y^2+12y\)
\(=-1\)
b,\((2x+5)(2x-7)-(-4x-3)^2=16\)
\(\Leftrightarrow 4x^2-14x+10x-35-(16x^2+24x+9)=16\)
\(\Leftrightarrow 4x^2-14x+10x-35-16x^2-24x-9=16\)
\(\Leftrightarrow -12x^2-28x-60=0\)
\(\Leftrightarrow -12(x^2+2.\dfrac{7}{6}x+\dfrac{49}{36})-\dfrac{131}{3}<0\) \(\forall x\)
\(\Rightarrow \) pt vô nghiệm.
\((8x^2+3)(8x^2-3)-(8x^2-1)^2=22\)
\(\Leftrightarrow 64x^4-9-(64x^4-16x^2+1)=22\)
\(\Leftrightarrow 16x^2=32\)
\(\Leftrightarrow x^2=2\)
\(\Leftrightarrow x=\pm\sqrt2\)