Prove or give a counterexample: Every positive integer can be expressed as the sum of three or fewer perfect squares. (A perfect square is an integer n for which there is an integer k with the property: n

Statement is incorrect

Step-by-step explanation:

Every positive integer cannot be expressed as the sum of three or fewer perfect squares.

Supposing the number 7 only squares less than are 0, 1  and   4

Clearly 7 can not be written using three or fewer of these numbers

It is proved

By taking Cube root of 7

= 1.912931183

Now By taking  

= 2.64575131

So both values 1.912931183 and 2.64575131 are not positive integers.

Hence the statement is incorrect.

no not all of them.

step-by-step explanation:

some of them have a square base.

x > 1.3

step by step:

8.5−0.9x> 9.8−1.9x

step 1: simplify both sides of the inequality.

−0.9x+8.5> −1.9x+9.8

step 2: add 1.9x to both sides.

−0.9x+8.5+1.9x> −1.9x+9.8+1.9x

1x+8.5> 9.8

step 3: subtract 8.5 from both sides.

1x+8.5−8.5> 9.8−8.5

1x> 1.3

step 4: divide both sides by 1.

1x/1 > 1.3/1