Solve 1/9^2+1leq1/8^2+1

$$\frac { 1 } { 9 ^ { 2 } + 1 } \leq \frac { 1 } { 8 ^ { 2 } + 1 }$$

Verify

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$\frac{1}{81+1}\leq \frac{1}{8^{2}+1}$$

Add 81 and 1 to get 82.

$$\frac{1}{82}\leq \frac{1}{8^{2}+1}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{1}{82}\leq \frac{1}{64+1}$$

Add 64 and 1 to get 65.

$$\frac{1}{82}\leq \frac{1}{65}$$

Least common multiple of 82 and 65 is 5330. Convert \frac{1}{82} and \frac{1}{65} to fractions with denominator 5330.

$$\frac{65}{5330}\leq \frac{82}{5330}$$

Compare \frac{65}{5330} and \frac{82}{5330}.

$$\text{true}$$