Question

please give solution of these 2questions fast please 14th and 15 question

Answer 1

14. We know that (a - b)^3 + (b - c)^3 + (c - a)^3 = 3(a - b) (b - c) (c - a) ... ( 1 ) 

So, (a^2 - b^2)^3 + (b^2 - c^2)^3 + (c^2 - a^2)^3 = 3(a^2 - b^2) (b^2 - c^2) (c^2 - a^2) ... ( 2 ) 

From ( 1 ) and ( 2 ),  We get

 (a^2-b^2)^3 + (b^2-c^2)^3 + (c^2-a^2)^3  / (a-b)^3 + (b-c)^3 + (c-a)^3)

= 3(a^2 - b^2) (b^2 - c^2) (c^2 - a^2)/ 3(a - b) (b - c) (c - a)

= 3(a+b) (a-b) (b+c) (b-c) (c+a) (c-a) / 3(a-b) (b-c) (c-a)

= (a + b) (b + c) (c + a). 




15. Given, AOP = 90 degrees and x : y : z = 1 : 3 : 5
i.e 1x + 3x + 5x = 90°
 9x = 90
 x = 90/9
 x = 10

 Then,
 y = 3 ×  10 = 30°
 z = 5 × 10 = 50°.



Hope this helps!