UPSC CDS 2 2022 Math Paper

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