Using the given pattern, find the missing numbers. 12+22+22=32 22+32+62=72 32+42+122=132 42+52+...2=212 52+...2+302=312 62+72+....2=....2

Given12+22+22=3222+32+62=7232+42+122=132Here, the pattern we can identify is that the third number is the product of first and second number.Because, for12+22+22=32Here, the third number is2=1×2The same rule holds for the next two equations as well.Similar way, the fourth term is1more than the third term.Because, for12+22+22=32Here, the fourth term is3=2+1The same rule holds for the next two equation as well (i) Now for,42+52+...2=212Since, here third term is product of first terms .That is third term is=4×5=20Therefore, the given equation can be written as42+52+202=212(ii) Similar way for ,52+...2+302=312Since, the third term(c=30)is product of first term (a=5) and second term (b=?).Thus,c=ab⇒b=ca=305∴b=6Hence, the given expression can be written as52+62+302=312(iii) For62+72+2=2Third term is product of first two terms.That is third term=6×7=42The fourth term is one more than the third term.That is fourth term is=42+1=43Therefore, the given expression is62+72+422=432