Mathematics: Which of the following tables shows the correct steps to transform x2 + 10x + 24 = 0 into the form (x − p)2 = q? [p and q are integers] a. step 1 x2 + 10x + 24 − 1 = 0 − 1 step 2 x2 + 10x + 23 = −1 step 3 (x + 5)2 = −1 b. step 1 x2 + 10x + 24 − 2 = 0 − 2 step 2 x2 + 10x + 22 = −2 step 3 (x + 5)2 = −2 c. step 1 x2 + 10x + 24 + 2 = 0 + 2 step 2 x2 + 10x + 26 = 2 step 3 (x + 5)2 = 2 d. step 1 x2 + 10x + 24 + 1 = 0 + 1 step 2 x2 + 10x + 25 = 1 step 3 (x + 5)2 = 1

Which of the following tables shows the correct

Ответ:

jose477

31.05.2020

Mathematics

x^2+10x+24=0

$\text{Use:}\\a^2+2ab+b^2=(a+b)^2$

$x^2+10x+24=x^2+2\cdot x\cdot5+24$

$\text{OK. We have}\\a^2=x^2\\2ab=2\cdot x\cdot5\to b=5\\\text{therefore}\ b^2\ \text{must be equal}\ 25=5^2.\\\text{we have:} 24. \text{We have to increase it by 1}\\ \text{Therefore the correct steps are in answer D.}$

$D.\ Step1\\x^2+10x+24=0\\\\x^2+2\cdot x\cdot5+24=0\\\\x^2+2\cdot x\cdot5+24+1=0+1\\\\Step2\\\\x^2+2\cdot x\cdot5+25=1\\\\x^2+2\cdot x\cdot5+5^2=1\\\\Step3\\\\(x+5)^2=1$

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