Question 187218
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1. The product of two consecutive odd numbers is 10 more than the square of the smaller number. 
Consecutive Odd numbers{{{system(x=smaller,x+2=bigger)}}}
Then,{{{(x)(x+2)=x^2+10}}}, EQN 1
{{{x^2+2x=x^2+10}}}--->{{{cross(x^2)+cross(2)x/cross(2)=cross(x^2)+cross(10)5/cross(2)}}}
{{{red(x=5)}}}, Smaller Number
{{{5+2=red(7)}}}, Bigger Number
Go back EQN 1 ---->{{{5*7=5^2+10}}}--->{{{35=25+10}}}--->{{{35=35}}}


2. If three times the smaller of two consecutive even integers is added to the larger, the result is 4 more than three times the larger.
Consecutive Even numbers{{{system(x=smaller,x+2=bigger)}}}
Then,{{{highlight(3x)+x+2=4+highlight(3(x+2))}}}, EQN 2
{{{4x+2=4+3x+6}}}---->{{{4x-3x=4+6-2}}}
{{{red(x=8)}}}, Smaller Number
Also, {{{8+2=red(10)}}}, Bigger number
Go back EQN 2 ----->{{{3*8+8+2=4+3(8+2)}}}---->{{{24+10=4+3(10)}}}-->{{{34=4+30}}}--->{{{34=34}}}


3. The product of two consecutive even numbers is 12 more than the square of the smaller number. 
Consecutive Even Numebrs{{{system(x=smaller,x+2=bigger)}}}
Then,{{{(x)(x+2)=12+x^2}}}, EQN 3
{{{x^2+2x=12+x^2}}}---->{{{cross(x^2)+cross(2)x/cross(2)=cross(12)6/cross(2)+cross(x^2)}}}
{{{red(x=6)}}}, Smaller number
Also,{{{6+2=red(8)}}}, Bigger Number
Go back EQN 3 ----> {{{(6)(8)=12+6^2}}}---->{{{48=12+36}}}--->{{{48=48}}}


Thank you,
Jojo</pre>
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