GIVEN: a + b + c = 11 ab + bc + ca = 36 CONCEPT: Algebra FORMULA USED: (a+b+c)2=a2+b2+c2+2āab+2ābc+2āca CALCULATION: a + b + c = 11 ab + bc + ca = 36 We know that: (a+b+c)2=a2+b2+c2+2āab+2ābc+2āca āa2+b2+c2=121ā72 āa2+b2+c2=49 āa2+b2=49āc2 We know that sum of two squares are always greater than or equal to zero ā0ā. a2+b2ā„0 ā49āc2ā„0 ā49ā„c2 āc2ā¤49 ācā¤7 ā“ Maximum value which ācā can take is 7.
