Question

Find the product of 2 numbers such that their sum multiplied by the sum of their squares is 5500 and their difference multiplied by the difference of their squares is 352.​

Answer 1

Step-by-step explanation:

Let x and y = the numbers

(x+y)(x2+y2)=5500(x+y)(x2+y2)=5500 ← Equation (1)

(x−y)(x2−y2)=352(x−y)(x2−y2)=352 ← Equation (2)

(x+y)(x2+y2)(x−y)(x2−y2)=5500352(x+y)(x2+y2)(x−y)(x2−y2)=5500352

(x+y)(x2+y2)(x−y)(x−y)(x+y)=1258(x+y)(x2+y2)(x−y)(x−y)(x+y)=1258

x2+y2(x−y)2=1258x2+y2(x−y)2=1258

8x2+8y2=125(x2−2xy+y2)8x2+8y2=125(x2−2xy+y2)

117x2−150xy+117y2=0117x2−150xy+117y2=0

(13x−9y)(9x−13y)=0(13x−9y)(9x−13y)=0

For 13x - 9y = 0

y=139xy=139x ← Equation (3)

From Equation (2)

(x−139x)[x2−(139x)2]=352(x−139x)[x2−(139x)2]=352

(−49x)(−8881x2)=352(−49x)(−8881x2)=352

(−49x)(−8881x2)=352(−49x)(−8881x2)=352

352729x3=352352729x3=352

x3=729x3=729

x=9x=9 answer

From Equation (3)

y=139(9)y=139(9)

y=13y=13

Answer 2

Answer:

(a+b)(a^2+b^2)=5500

(a-b)(a^2-b^2)=352

(a-b)^2(a+b)=352

Then:

5500/(a^2-b^2)=352/(a-b)^2

Then(a-b)^2 must be a factor of 352

So,

(a-b)^2=4 or (a-b)^2=16

But it can't be 4,(a-b)^2=16

Then:a^2 +b^2=250

(a-b)=4

So,the solution is a=13 and b=9.

Hope it helps,

Step-by-step explanation:

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