Q1 Consider atriangle ABC with G as its centroid. If vectors GB and GC are inclined at an obtuse angle,then prove that 5a²>b²+c².

Q2 If  IS THE AREA OF A TRIANGLE ABC and length of its two sides are 3 and 5. If c is the third side then prove that:           

<=c²+16c+64/12root3

SALUTES ASSURED TO ALL CORRECT SOLUTIONS.

The second question has the answer in the following link ..

http://www.goiit.com/posts/list/trignometry-sot-challenge-46259.htm#228738

2) For a triangle of given perimeter the area is maximum for a equilateral triangle.

In the triangle perimeter is (c+5+3)=c+8

For the equilateral triangle side is (c+8)/3

so, area of given triangle is

But the equality can never be holded as 2 sides are givenas 3,5