Question on Perfect Square Formula

[senseimichael]

Given that [math](a-b)=20.25[/math] and [math]ab=3[/math] , find the value of [math](1/4)(a+b)^2[/math]
I tried expanding out [math](a+b)^2=a^2+2ab+b^2[/math] but could not find any way to deal with [math]a^2+b^2[/math] after this! Have I encountered yet again another teacher who set an unsolveable question?

 

[Dr.Peterson]

Given that [math](a-b)=20.25[/math] and [math]ab=3[/math] , find the value of [math](1/4)(a+b)^2[/math]
I tried expanding out [math](a+b)^2=a^2+2ab+b^2[/math] but could not find any way to deal with [math]a^2+b^2[/math] after this! Have I encountered yet again another teacher who set an unsolveable question?

No, it's perfectly solvable; it's just not as immediate as you were hoping.

What happens if you square the first equation? How is that related to what you want to find?

 

[BigBeachBanana]

[math]a^2+2ab+b^2=a^2+2ab+b^2-2ab+2ab=(a-b)^2+4ab[/math]

 

[senseimichael]

No, it's perfectly solvable; it's just not as immediate as you were hoping.

What happens if you square the first equation? How is that related to what you want to find?

I got it! Yes, it has to be Dr Petersen! Thank you!

[math]a^2+2ab+b^2=a^2+2ab+b^2-2ab+2ab=(a-b)^2+4ab[/math]

Yup, I got it the moment Dr Petersen mentioned it...but this one is good! Thank you!