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a) \(56^2+44^2+2.56.44=56^2+2.56.44+44^2=\left(56+44\right)^2=100^2=10000\)
b) \(36^2+64^2+72.64=36^2+2.36.64+64^2=\left(36+64\right)^2=100^2=10000\)
c) \(136^2+36^2-72.136=136^2-2.36.136+36^2=\left(136-36\right)^2=100^2=10000\)
a) $56^2+44^2+2.56.44=56^2+2.56.44+44^2=\left(56+44\right)^2=100^2=10000$562+442+2.56.44=562+2.56.44+442=(56+44)2=1002=10000
b) $36^2+64^2+72.64=36^2+2.36.64+64^2=\left(36+64\right)^2=100^2=10000$362+642+72.64=362+2.36.64+642=(36+64)2=1002=10000
c) $136^2+36^2-72.136=136^2-2.36.136+36^2=\left(136-36\right)^2=100^2=10000$
\(\left[x-\frac{3}{2}\right]^3=\frac{1}{64}\)
\(\Leftrightarrow\left[x-\frac{3}{2}\right]^3=\left[\frac{1}{4}\right]^3\)
\(\Leftrightarrow x-\frac{3}{2}=\frac{1}{4}\Leftrightarrow x=\frac{1}{4}+\frac{3}{2}=\frac{7}{4}\)
\(\left[x+\frac{3}{2}\right]^2=\frac{9}{49}\)
\(\Leftrightarrow\left[x+\frac{3}{2}\right]^2=\left[\frac{3}{7}\right]^2\)
\(\Leftrightarrow x+\frac{3}{2}=\pm\frac{3}{7}\)
\(\Leftrightarrow\orbr{\begin{cases}x+\frac{3}{2}=\frac{3}{7}\\x+\frac{3}{2}=-\frac{3}{7}\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=-\frac{15}{14}\\x=-\frac{27}{14}\end{cases}}\)
a)6x2-12x=6x(x-2)
b)x2-12x+36=(x-6)2
c)8xy-16x2-y2=-(4x-y)2
d)125x3+1/64=(5x+1/4)(25x2-5/4x+1/16)
e)1/64x2+1/64=1/64(x2+1)
a, 6x^2 - 12x = 6x ( x-2)
b, x^2 - 12x + 36 = x^2 - 2.x.6 + 36 = ( x -6)^2
c, 8xy - 16x^2 - y^2 = - [ 16x^2 - 8xy + y^2) = - (4x - y)^2
d, 125y^3 + 1/64 = ( 5y + 1/4)(25y^2 - 5/4y + 1/16)
e, 1/64 x^2 + 1/64 = 1/64( x^2+1)
a, \(\left(x-y+4\right)^2-\left(2x+3y-1\right)^2=\left(x-y+4+2x+3y-1\right)\left(x-y+4-2x-3y+1\right)\)
\(=\left(3x+2y+3\right)\left(-x-4y+5\right)\)
b, \(x^6+y^6=\left(x^2\right)^3+\left(y^2\right)^3=\left(x^2+y^2\right)\left(x^4-x^2y^2+y^4\right)\)
c, \(x^{16}-1=\left(x^2\right)^8-1=\left[\left(x^2\right)^4\right]^2-1=\left(x^8-1\right)\left(x^8+1\right)\)
\(36-\left(-48\right)+\left(-48\right)+64=36+48-48+64=\left(48-48\right)+\left(36+64\right)=100\)
Ta có: \(36^2+64^2+2\cdot36\cdot64=\left(36+64\right)^2=100^2=10000\)