4/9x²-x+9/16=0 Δ=b²-4ac=1-4*4/9*9/16=1-1=0 x0=-b/2a=1:2*4/9=1*9/8=9/8 x³+10x²+25x=0 x(x²+10x+25)=0 Δ=100-100=0 x=0 ∨ x=-10/2=-5 c] 0=3x²-12x 3x(x-4)=0 x=0 ∨x=4 d] 16x²-1=0 (4x+1)(4x-1)=0 x=-1/4 ∨ x=1/4
[latex]a)\\ frac49x^2-x+frac9{16}=0\\(frac23x)^2-2cdotfrac23xcdotfrac34+(frac34)^2=0\\(frac23x-frac34)^2=0\\ frac23x-frac34=0\\ frac23x=frac34 /:frac23\\x=frac34 cdot frac32\\x=frac98=1frac18[/latex] [latex]b)\\ x^3+10x^2+25x=0\\x(x^2+10x+25)=0 \\x(x^2+2cdot xcdot5+5^2)=0\\x(x+5)^2=0\\x=0quadveequad x+5=0 \\x=0quadveequad x=-5[/latex] [latex]c)\\ -3x^2=-12x /:(-3)\\x^2=4x\\x^2-4x=0\\x(x-4)=0\\x=0quadveequad x-4=0\\x=0quadveequad x=4[/latex] [latex]d)\\ 16x^2-1=0\\(4x)^2-1^2=0\\(4x-1)(4x+1)=0\\ 4x-1=0quadveequad 4x+1=0\\4x=1 /:4quadveequad 4x=-1 /:4\\~ x=frac14qquad veeqquad x=-frac14[/latex]
