Pythagoras theorem: It states that In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides. Let, BD=3,AD=4AB=5 ⇒CD=1(∵DB=3CD) ⇒AC=√(16+1)=√17( From Pythagoras theorem )
(AB+AC)(AB−AC)=AB2−AC2 ⇒(AB+AC)(AB−AC)=52−(√17)2=8 From option (1) 2(AB+AC)(AB−AC)=BC2 ⇒2×8=(3+1)2 ⇒16=16 ∴ The required value is 2(AB+AC)(AB−AC)=BC2