the product of two consecutive integers is 8 less than 8 times their sum. what are the integers?
N nativewind New member Joined Oct 16, 2009 Messages 1 Oct 16, 2009 #1 the product of two consecutive integers is 8 less than 8 times their sum. what are the integers?
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Oct 16, 2009 #2 Hello, nativewind! The product of two consecutive integers is 8 less than 8 times their sum. What are the integers? Click to expand... We have two consecutive integers. Let x\displaystyle xx = first integer, x+1\displaystyle x+1x+1 = next integer. . . Product of the two integers ⏟x(x+1) is ⏟= 8 times ⏟8× their sum ⏟x+(x+1) minus 8 ⏟− 8\displaystyle \underbrace{\text{ Product of the two integers }}_{x(x+1)} \underbrace{\text{ is }}_{=} \underbrace{\text{ 8 times }}_{8 \times} \underbrace{\text{ their sum }}_{x+(x+1)} \underbrace{\text{ minus 8 }}_{-\;8}x(x+1) Product of the two integers = is 8× 8 times x+(x+1) their sum −8 minus 8 The equation is: x(x+1) = 8(2x+1)−8\displaystyle \text{The equation is: }\;x(x+1) \;=\;8(2x+1) - 8The equation is: x(x+1)=8(2x+1)−8 Now solve the quadratic . . .
Hello, nativewind! The product of two consecutive integers is 8 less than 8 times their sum. What are the integers? Click to expand... We have two consecutive integers. Let x\displaystyle xx = first integer, x+1\displaystyle x+1x+1 = next integer. . . Product of the two integers ⏟x(x+1) is ⏟= 8 times ⏟8× their sum ⏟x+(x+1) minus 8 ⏟− 8\displaystyle \underbrace{\text{ Product of the two integers }}_{x(x+1)} \underbrace{\text{ is }}_{=} \underbrace{\text{ 8 times }}_{8 \times} \underbrace{\text{ their sum }}_{x+(x+1)} \underbrace{\text{ minus 8 }}_{-\;8}x(x+1) Product of the two integers = is 8× 8 times x+(x+1) their sum −8 minus 8 The equation is: x(x+1) = 8(2x+1)−8\displaystyle \text{The equation is: }\;x(x+1) \;=\;8(2x+1) - 8The equation is: x(x+1)=8(2x+1)−8 Now solve the quadratic . . .
