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mỗi phân số cộng thêm 1 ta có
\(\frac{x+66}{65}+\frac{x+66}{63}=\frac{x+66}{61}+\frac{x+66}{59}\)
rồi đặt x+66 làm thừa số chung sau đó giải tiếp
\(\frac{x-1}{65}+\frac{x-3}{63}=\frac{x-5}{61}+\frac{x-7}{59}\)
\(\Rightarrow\frac{x-1}{61}-1\frac{x-3}{63}+-1=\frac{x-5}{61}-1+\frac{x-7}{59}-1\)
\(\Rightarrow\frac{x-66}{65}+\frac{x-66}{63}=\frac{x-66}{61}+\frac{x-66}{59}\)
\(\Rightarrow\left(x-66\right)\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\)
\(\Rightarrow x=66\)
a) \(\left|x-5\right|-\left|x-7\right|=\left|x-5\right|-\left|x-5-2\right|\ge\left|x-5\right|-\left(\left|x-5\right|-2\right)=2\)
Dấu \(=\)khi \(-2\left(x-5\right)\ge0\Leftrightarrow x\le5\).
b) \(\left|125-x\right|+\left|x+65\right|\ge\left|125-x+x+65\right|=190\)
Dấu \(=\)khi \(\left(125-x\right)\left(x+65\right)\ge0\Leftrightarrow-65\le x\le125\).
\(\dfrac{x-1}{65}+\dfrac{x-3}{63}=\dfrac{x-5}{61}+\dfrac{x-7}{59}\)
\(\Leftrightarrow\dfrac{x-1}{65}-1+\dfrac{x-3}{63}-1=\dfrac{x-5}{61}-1+\dfrac{x-7}{59}-1\)
\(\Leftrightarrow\dfrac{x-66}{65}+\dfrac{x-66}{63}=\dfrac{x-66}{61}+\dfrac{x-66}{59}\)
\(\Leftrightarrow\left(x-66\right)\left(\dfrac{1}{65}+\dfrac{1}{63}-\dfrac{1}{61}-\dfrac{1}{59}\right)=0\)
\(\Leftrightarrow x-66=0\)
\(\Leftrightarrow x=66\)
Vậy x=66.
Ta có : \(\frac{x-1}{65}+\frac{x-3}{63}=\frac{x-5}{61}=\frac{x-7}{59}\)
\(\Leftrightarrow\left(\frac{x-1}{65}-1\right)+\left(\frac{x-3}{63}-1\right)=\left(\frac{x-5}{61}-1\right)+\left(\frac{x-7}{59}-1\right)\)
\(\Leftrightarrow\frac{x-66}{65}+\frac{x-66}{63}=\frac{x-66}{61}+\frac{x-66}{59}\)
\(\Leftrightarrow\frac{x-66}{65}+\frac{x-66}{63}-\frac{x-66}{61}-\frac{x-66}{59}=0\)
\(\Leftrightarrow\left(x-66\right)\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)=0\)
Mà ; \(\left(\frac{1}{65}+\frac{1}{63}-\frac{1}{61}-\frac{1}{59}\right)\ne0\)
Nên x - 66 = 0
=> x = 66
5+x*x+65
= x*x+ 70
h nhé
cảm ơn
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