Question

Chi biết \(\dfrac{a}{c}=\dfrac{b}{d}=k\) . Tính giá trị tỉ số \(\dfrac{c.a^2+d.b^2}{c^3+d^3}\) theo k

Answer 1

a/c=b/d=k

=>a=ck; b=dk

=>\(\dfrac{c\cdot a^2+d\cdot b^2}{c^3+d^3}\)

\(=\dfrac{c\cdot c^2k^2+d\cdot d^2k^2}{c^3+d^3}=k^2\)

Answer 2

đặt \(\dfrac{a}{c}\) =\(\dfrac{b}{d}=k\)

\(\Rightarrow a=c\times k\)

\(b=d\times k\)

\(\dfrac{c.\left(c.k\right)^2+d.\left(d.k\right)^2}{c^3+d^3}\)

=\(\dfrac{c^3.k^2+d^3.k^2}{c^3+d^3}\)

=\(\dfrac{k^2\left(c^3+d^3\right)}{1\left(c^3+d^3\right)}\)=k²