For any three positive real numbers a ,   b and c . If 9 25 a 2 + b 2 + 25 c 2 - 3 a c = 15 b 3 a + c . Then

Question

For any three positive real numbers a , &#160; b and c . If 9 25 a 2 + b 2 + 25 c 2 - 3 a c = 15 b 3 a + c . Then

Aicharya · Accepted Answer

225 a 2 + 9 b 2 + 25 c 2 - 75 a c - 45 a b - 15 b c = 0 &#8658; &#160; &#160; 2 15 a 2 + 3 b 2 + 5 c 2 - 15 a 5 c - 15 a 3 b - 3 b 5 c = 0 &#160; &#8658; &#160; &#160; 2 15 a 2 + 2 3 b 2 + 2 5 c 2 - 2 15 a 5 c - 2 15 a 3 b - 2 3 b 5 c = 0 &#8658; 15 a - 3 b 2 + 3 b - 5 c 2 + 5 c - 15 a 2 = 0 &#8658; 15 a - 3 b = 3 b - 5 c = 5 c - 15 a = 0 &#8658; 15 a = 3 b = 5 c &#8658; &#160; &#160; a 1 = b 5 = c 3 = k &#8658; &#160; &#160; &#160; a = k , &#160; b = 5 k , &#160; c = 3 k &#8658; &#160; &#160; a , &#160; c , &#160; b &#160; a r e &#160; i n &#160; A . P . &#8658; &#160; &#160; b , &#160; c , &#160; a &#160; a r e &#160; i n &#160; A . P .

For any three positive real numbers a ,   b and c . If 9 25 a 2 + b 2 + 25 c 2 - 3 a c = 15 b 3 a + c .…

Solution

For any three positive real numbers a , &#160; b and c . If 9 25 a 2 + b 2 + 25 c 2 - 3 a c = 15 b 3 a + c .…

Solution

For any three positive real numbers a , b and c . If 9 25 a 2 + b 2 + 25 c 2 - 3 a c = 15 b 3 a + c .…