Find the value of √70+√4896+√70−√4896√70+√4896+√70−√4896.
Answer:
1212
- We need to find the value of √70+√4896+√70−√4896√70+√4896+√70−√4896
Let a=√70+√4896a=√70+√4896 and b=√70−√4896b=√70−√4896 - a2+b2=70+√4896+70−√4896⟹a2+b2=140…(1)Andab=√(70+√4896)(70−√4896)⟹ab=√702−4896⟹ab=√4⟹ab=2…(2)
- (a+b)2=a2+b2+2ab⟹(a+b)2=140+2×2[From eq(1) and eq(2)]⟹(a+b)2=144⟹a+b=12
- Hence, the value of √70+√4896+√70−√4896 is 12.