Question

1) If a+b=5&a-b=4,find  a²+b²
2)If (x+a)*(x+b)=x²-5x-300,find the values of a²+b²

Answer 1

 1).   a+b = 5   ----------(1)
        And,  a-b = 4 --------(2)
On adding equation (1) and (2)
    ⇒  2a = 9
     ⇒   a = 9/2
From equation (1),
     b = 5 - 9/2 
so,  b = 1/2
Now,    a²+b² = (9/2)²+(1/2)²
            a²+b² =  82/4 = 20.5

2). (x+a)(x+b) = x²-5x-300
     ⇒  x²+(a+b)x +ab = x²-5x-300
    On equating the co-efficient of x  and constant term,
        a+b = -5 ----------(1)
and,    ab = -300  ---------(2)
From equation (1)
          a+b = -5
squaring both side of this eqn
       ⇒ (a+b)² =  -5
       ⇒ a²+b²+2ab = -5
Put the value of ab from eqn (2)
            a²+b²+2(-300) = -5
      ⇒   a²+b² -600 = -5
      ⇒   a²+b² = -5+600 = 595