First find the factors of 20
1 & 20
2 & 10
4 & 5
-1 & -20
-2 & -10
-4 & -5
Now find the pairs that have a difference of 1
-4 & -5
4 & 5
Hello :
<span>√(4x+13) = 2x-1......(1)
note : if ( a=b) so (a² = b²)
if : (</span>√(4x+13) )²= (2x-1)² so : 4x+13 = 4x²-4x+1
4x²-8x-12 = 0
x²-2x-3 = 0
(x+1)(x-3) = 0
x+1 = 0 or x-3=0
x= -1 or x=3
if : x= -1 : <span>√(4(-1)+13) = 2(-1)-1
</span>√9 =-3 but √9 =3
3 = -3 impossible ( -1 is not solution of equation (1)
if : x = 3 : √(4(3)+13) = 2(3)-1
5 = 5 ( right) conclusion : one solution : 3
From the double-angle identity,
we can rewritte our given equation as:
By factoring 2cosx on the left hand side, we have
This equation has 2 solutions when
From equation (A), we obtain
and from equation (B), we have
On the other hand, we can find one more solution from the original equation by substituting x=0, that is,
then, x=0 is another solution. In summary, we have obtained the following solutions:
However, the intersection of the last set is empty. So the unique solution is x=0 as we can corroborate on the following picture:
Therefore, the solution set is: {0}