If X2 + Y2 = 100 and X : Y = 4 : 3, then what is the value of X2 − Y2?

If X² + Y² = 100

X : Y = 4 : 3,

then what is the value of X² − Y²?

Let the value of X and Y be 4m and 3m

Given,

X² + Y² = 100

= 16m² + 9m² = 100

= m² = \(\frac{100}{25}\) = 4

= a = 2

= X² – Y² = 16m² – 9m² = 7m² = 7 × 4 = 28