Question

If a+ b=7 and a square + b square =29 find the value of a and b

Answer 1

Step-by-step explanation:

given- a+b=7.....(1) and a²+b²=29

using identity- (a+b)²=a²+2ab+b², we get-

(7)²=29+2ab (substituting the given values)

49-29=2ab

20=2ab

10=ab......(2)

using(1) in (2) we get-

10=a(7-a)

10=7a-a²

=> a²-7a+10=0

now solving this equation-

a²-5a-2a+10=0

a(a-5) -2(a-5)=0

(a-5)(a-2)=0

a=5, 2

now, further solving-

case1-

when a=5

then,b=2

case2-

when a=2

then,b=5

hope it helps!