Math Help 10 points TONIGHT!!!!!!!!!!!!

THe sum of the squares of 2 whole #'s is 160. The product of the numbers is 48. What is the positive difference between the two whole #'s.

Just tell me the answer please:)

2 whole numbers that when squared get 160 are 12 and 4. 12^2 = 144 and 4^2 = 16. 144+16=160. The product of the two numbers is 48 (12x4=48). The positive difference between 12 and 4 is 8. Hope I helped!

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Let m and n be the two whole numbers we are looking for.
Then "THe sum of the squares of 2 whole #'s is 160".   ⇒   m²+n² = 160.
And, "The product of the numbers is 48".   ⇒   mn = 48

So, the solution to this problem is the solution to this system of simultaneous equations:
➊ m²+n² = 160
➋ mn = 48   ⇒   m = 48/n            ← Now, substitute this into ➊ and solve for n

➊                m²+n² = 160
           (48/n)²+n² = 160            ← Multiply both sides by n²
                 48²+n⁴ = 160n²
    n⁴-160n²+2304 = 0
(n²)²-160n²+2304 = 0            ← This is a quadratic equation in n²

Using the Quadratic Equation, we get:

           160 ± √[160² - (4)(1)(2304)]            160 ± 128
n² = —————————————— = —————— = 72, 16
                               2·1                                       2


n = √(72), √(16)
n = √(72), 4            ← Note that √(72) is not a whole number
n = 4            ← Now, substitute this into ➊ or ➋ to solve for m


➋ mn = 48
     4n = 48
       n = 12



The two numbers are 4 and 12.
The difference between them is 8            ← ANSWER



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12 and 4 are the numbers
12^2+4^2=160
12*4=48
there difference is 8.

The numbers are 4 and 12 the square root of 4 is 16 and the square root of 12 is 144 so 144 + 16 = 160
so 12-4 =8 so that is the answer 8!