Cho : \(\dfrac{a}{c}=\dfrac{c}{b}.CMR:\\ a,\dfrac{a^2+c^2}{b^2+c^2}=\dfrac{a}{b}\\ b,\dfrac{b^2-a^2}{a^2+c^2}=\dfrac{b-a}{a}\)
cho a/b=c/d
chứng minh :
2a/a+b=2c/c+a
a-b/2a+b=c-d/2c-d
a/a^2+b^2=c/c^2+d^2
a+b/a^2-b^2=c+d/c^2-d^2
Cho c2==ab . Chứng minh rằng :
a) \(\dfrac{a^{2^{ }}+c^2}{b^{2^{ }}+c^{2^{ }}}=\dfrac{a}{b}\)
b)\(\dfrac{b^{2^{ }}-a^{2^{ }}}{a^{2^{ }}+c^2}=\dfrac{b-a}{a}\)
Cho \(\dfrac{a}{b}=\dfrac{c}{d} \) . Chứng minh :
a, \(\dfrac{a^2+c^2}{b^2+d^2} =\dfrac{ac}{bd}\)
b, \(\dfrac{a^2+c^2}{b^2+d^2} = \dfrac{a^2-c^2}{b^2-d^2}\)
c, \(\dfrac{(a+c)^2}{(b+d)^2} = \dfrac{(a-c)^2}{b-d)^2}\)
d, \(\dfrac{a^2+b^2}{a^2-b^2} = \dfrac{c^2+d^2}{c^2-d^2}\)
e, \(\dfrac{(a-b )^2}{(c-d)^2} = \dfrac{a^2+b^2}{c^2+d^2}\)
cho a + b ≠ c ; b ≠ c; c2 = 2( ac + bc - ab ). Chứng minh rằng \(\dfrac{a^2+\left(a-c\right)^2}{b^2+\left(b-c\right)^2}=\dfrac{a-c}{b-c}\)
cho a/b=c/d=h
C/m: ( a+b/ c+d )^2 = a^2 + b^ 2 / c^2 + d^2
Cho : \(\dfrac{a}{c}=\dfrac{c}{b}\) CMR :
a.\(\dfrac{a^2+c^2}{b^2+c^2}=\dfrac{a}{b}\)
b.\(\dfrac{b^2-a^2}{a^2+c^2}=\dfrac{b-a}{a}\)
Cho các số thực a, b, c thỏa mãn a+b+c = 6 và a^2+b^2+c^2 = 12. Chứng minh rằng a=b=c=2
Cho \(\dfrac{a}{c}=\dfrac{c}{b}\) chứng minh rằng : \(\dfrac{b^2-a^2}{a^2+c^2}=\dfrac{b-a}{a}\)