Question on Perfect Square Formula

[senseimichael]

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

 

[Dr.Peterson]

Given that $$(a-b)=20.25$$ and $$ab=3$$ , find the value of $$(1/4)(a+b)^2$$
I tried expanding out $$(a+b)^2=a^2+2ab+b^2$$ but could not find any way to deal with $$a^2+b^2$$ 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]

$$a^2+2ab+b^2=a^2+2ab+b^2-2ab+2ab=(a-b)^2+4ab$$

 

[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!

$$a^2+2ab+b^2=a^2+2ab+b^2-2ab+2ab=(a-b)^2+4ab$$

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