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\(A=0.5\cdot4\sqrt{3-x}-\sqrt{3-x}-2\sqrt{3}+1=\sqrt{3-x}-2\sqrt{3}+1\) (xác định khi x=<3)
a)thay \(x=2\sqrt{2}\)vào a ra có
\(\sqrt{3-2\sqrt{2}}-2\sqrt{3}+1=\sqrt{\left(\sqrt{2}-1\right)^2}-2\sqrt{3}+1\)
\(=\sqrt{2}-1+2\sqrt{3}+1=\sqrt{2}+2\sqrt{3}\)
Để A=1<=> \(\sqrt{3-x}-2\sqrt{3}+1=1\\ \Leftrightarrow\sqrt{3-x}-2\sqrt{3}+1-1=0\\ \Leftrightarrow\sqrt{3-x}-2\sqrt{3}=0\\ \Leftrightarrow3-x=12\Leftrightarrow x=-9\)
\(-6a^2+17a-10=-6a^2+12a+5a-10\)
\(=-6a\left(a-2\right)+5\left(a-2\right)=\left(a+2\right)\left(5-6a\right)\)
a/ \(x^2+5\sqrt{x}+6=x^2+2\sqrt{x}+3\sqrt{x}+6\)
\(=\sqrt{x}\left(\sqrt{x}+2\right)+3\left(\sqrt{x}+2\right)=\left(\sqrt{x}+2\right)\left(\sqrt{x}+3\right)\)
b/ \(x^2+4\sqrt{x}+3=x^2+\sqrt{x}+3\sqrt{x}+3\)
\(=\sqrt{x}\left(\sqrt{x}+1\right)+3\left(\sqrt{x}+1\right)=\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)\)
c/ k bik làm
\(4x^4-37x^2+9=4x^4-36x^2-x^2+9=4x^2\left(x^2-9\right)-\left(x^2-9\right).\)
\(=\left(x^2-9\right)\left(4x^2-1\right)=\left(x-3\right)\left(x+3\right)\left(2x-1\right)\left(2x+1\right)\)
Đặt t = x2
đa thức trở thành 4t2 - 37t + 9
= 4t2 - t - 36t + 9
= ( 4t2 - 36t ) - ( t - 9 )
= 4t( t - 9 ) - ( t - 9 )
= ( t - 9 )( 4t - 1 )
= ( x2 - 9 )( 4x2 - 1 )
= ( x - 3 )( x + 3 )( 2x - 1 )( 2x + 1 )
\(3\times y^2-12\times y+12\times\)
\(=3\times\cdot\left(y^2-4y+4\right)\)
\(=3\times\cdot\left(y^2-2\cdot2y+2^2\right)\)
\(=3\times\cdot\left(y-2\right)^2\)
\(3xy^2-12xy+12x\)
\(=3x\left(y^2-4y+4\right)\)
\(=3x\left(y-2\right)^2\)
\(3xy^2-12xy+12x\)
\(=3x\left(y^2-4y+4\right)\)
\(=3x\left(y-2\right)^2\)
mk nghĩ đúng đó
hc tốt
E CẢM ƠN CÁC ANH Ạ
\(3xy^2-12xy+12x\)
\(=3x.\left(y^2-4y+4\right)\)
\(=3x.\left(y-2\right)^2\)
Study well
\(3xy^2-12xy+12x\)
\(3x\left(y^2-4y+4\right)\)
\(=3x\left(y-2\right)^2\)