Question

Tìm a, b, c, biết:
a
2
=
b
3
=
c
4
và a
2 − b
2 + 2c
2 = 108

Answer 1

Đặt \(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}=k\)

=>a=2k; b=3k; c=4k

\(a^2-b^2+2c^2=108\)

=>\(\left(2k\right)^2-\left(3k\right)^2+2\cdot\left(4k\right)^2=108\)

=>\(4k^2-9k^2+2\cdot16k^2=108\)

=>\(27k^2=108\)

=>\(k^2=4\)

=>\(\left[\begin{array}{l}k=2\\ k=-2\end{array}\right.\)

TH1: k=2

=>\(\begin{cases}a=2\cdot2=4\\ b=3\cdot2=6\\ c=4\cdot2=8\end{cases}\)

TH2: k=-2

=>\(\begin{cases}a=2\cdot\left(-2\right)=-4\\ b=3\cdot\left(-2\right)=-6\\ c=4\cdot\left(-2\right)=-8\end{cases}\)