Bài 123
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c: -62+x=-14+46
=>\(x-62=46-14=32\)
=>\(x=32+62=94\)
d: \(25+\left(x-5\right)=-123-\left(15-123\right)\)
=>\(x-5+25=-123-15+123\)
=>\(x+20=-15\)
=>\(x=-15-20=-35\)
B) 2x + (-416) - (231 - 416 )
= 2x - 416 - 231 + 416
= 2x - ( 416 +231 - 416 )
= 2x - 231
D) 211-(123-x)+(123-211)
= 211 - 123 + x + 123 - 211
= ( 211 - 123 +123 - 211 )+ x
= 0+ x
= x
b) 2x + (-461) - (231 - 416)
= 2x - 461 - (231 - 416)
= 2x - 461 + 185
= 2x - 276
d) 211 - (123 - x) + (123 - 211)
= 211 - 123 + x + 123 - 211
= (211 - 211) + (-123 + 123) + x
= 0 + 0 + x
= x
\(a,100.123-123.100\)
\(=100.\left(123-123\right)\)
\(=100.0\)
\(=0\)
\(b,10.30+70.10\)
\(=10.\left(30+70\right)\)
\(=10.100\)
\(=1000\)
a) 100 x 123 - 123 x 100
= 100 x ( 123 - 123 )
= 100 x 0
=100
b) 10 x 30 + 70 x 10
= 10 x ( 30 + 70)
= 10 x 10
= 100
\(1,\\ a,=5\sqrt{2}-12\sqrt{2}+10\sqrt{2}=3\sqrt{2}\\ b,=\dfrac{\sqrt{5}-2}{5-4}-\dfrac{\sqrt{5}\left(\sqrt{3}-2\right)}{\sqrt{3}-2}=\sqrt{5}-2-\sqrt{5}=-2\\ c,=3\sqrt{3}-\left|1-\sqrt{3}\right|-\dfrac{6\sqrt{3}}{3}=3\sqrt{3}-\left(\sqrt{3}-1\right)-2\sqrt{3}=1\)
\(2,\\ a,P=\left(\dfrac{1}{\sqrt{a}-2}+\dfrac{1}{\sqrt{a}+2}\right)\left(1+\dfrac{2\left(\sqrt{a}-2\right)}{a-2\sqrt{a}}\right)\left(a>0;a\ne4\right)\\ P=\dfrac{\sqrt{a}+2+\sqrt{a}-2}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\cdot\left[1+\dfrac{2\left(\sqrt{a}-2\right)}{\sqrt{a}\left(\sqrt{a}-2\right)}\right]\\ P=\dfrac{2\sqrt{a}}{\left(\sqrt{a}-2\right)\left(\sqrt{a}+2\right)}\cdot\dfrac{\sqrt{a}+2}{\sqrt{a}}=\dfrac{2}{\sqrt{a}-2}\)
\(b,\sqrt{4x+12}-3\sqrt{x+3}+\sqrt{16x+48}=9\left(x\ge-3\right)\\ \Leftrightarrow2\sqrt{x+3}-3\sqrt{x+3}+4\sqrt{x+3}=9\\ \Leftrightarrow3\sqrt{x+3}=9\Leftrightarrow\sqrt{x+3}=3\\ \Leftrightarrow x+3=9\Leftrightarrow x=6\left(tm\right)\)
Bài 3:
Ta có: \(\sin\widehat{B}=\dfrac{4}{5}\)
nên \(\dfrac{AC}{BC}=\dfrac{4}{5}\)
hay BC=15(cm)
Áp dụng định lí Pytago vào ΔABC vuông tại A, ta được:
\(BC^2=AB^2+AC^2\)
hay AB=3(cm)