Question

D. 133
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Q 26 Sum of two numbers is 17 and the difference
between their squares is 68. Determine the
product of the numbers.
Ops: A
62.85
B.
72.75
C.
92.75​

Answer 1

Answer:

x²+y²=68  

(x−y)²=36  

x²−2xy+y²=36  

x²+y²−x²+2xy−y²=68−36  

2xy=32  

2xy2=322  

xy=16  

xy=16

x-y=6

x=6+y

y(y+6)=16  

y²+6y−16=16−16  

y²+6y−16=0  

(y−2)(y+8)=0  

So y can either equal 2 or -8, and x can either equal -2 or 8.

Verifying:

8²+2²  

=> 64+4=68  

(−8)²+(−2)²  

=> 64+4=68  

(8)²−2(8×2)+(2)²  

=> 64−32+4=36  

(−8)²−2(−8×−2)+(−2)²  

=> 64−32+4=36  

xy=16  

−8×−2=16  

8×2=16  

Thus the product of the numbers is 16.

Step-by-step explanation: