If a2 + b2 =2 and c2 + d2 = 1, then the value of (ad-bc)2 +(ac+bd)2 is: - Maths - Polynomials

Question

If a2 + b2 =2 and c2 +
d2 = 1, then the value of (ad-bc)2
+(ac+bd)2 is:

Vishvesh Kumar · Accepted Answer

Given that (a2+b2) =2 ,(c2+d2)=1So (ad-bc)2+(ac+bd)2 =(ad)2-2adbc+(bc)2+(ac)+2acbcd+(bd)2    by the formula (x±y)2=x2±2xy+y2=a2d2-2abcd+b2c2+a2c2+2abcd+b2d2=a2d2+b2c2+a2c2+b2d2=a2(c2+d2)+b2(c2+d2)=(c2+d2)(a2+b2) =1×2=2