Question

If cl ab and (b, c) = 1 then prove that c|a .​

Answer 1

Answer: Given, a+b+c=0

and ∣a∣=5,∣b∣=3,∣c∣=7

⇒a+b=c

On squaring both sides, we get

(a+b)

2

=(−c)

2

⇒∣a+b∣

2

=∣c∣

2

⇒∣a∣

2

+∣b∣

2

+2a⋅b=∣c∣

2

(∵θ be the angle between a and b)

⇒(5)

2

+(3)

2

+2∣a∣∣b∣cosθ=(7)

2

⇒25+9+2⋅5⋅3cosθ=49

⇒30cosθ=15

⇒cosθ=

2

1

​

=cos60

∘

⇒θ=

3

π

​

Step-by-step explanation: