 Hello folks once again welcome to another video session on Serds and this in this session. We are going to discuss about equality of two Serds Okay, so what is meant by equality of two Serds or when what is the condition when two Serds are equal? Let us say we have two Serds a plus root b and X plus root y okay where where a b x and y all are Rational numbers all are rational numbers and and b and y are Not perfect Squires Okay, perfect Squires, why am I taking this condition? We'll see a little later, but a and b a b x and y all are rational numbers and B and b and y are not perfect square. That means what root of b and root of y are Irrational pure irrational Irrational numbers Okay, so now a plus root b. So we say that if a plus or rather a plus root b is Equal to x plus root y if And only if a is equal to x and b is equal to y This is this is what is meant by equality of two Serds. Let's take an example So let us say if you have x plus root y is equal to 3 minus 2 root 7 3 plus root 7 then x is equal to 3 and Y is equal to 7 This is what is meant by equality of two Serds. Let us now try to prove it Okay So if let us say a is equal to x and b is equal to y that is what our assertion is Let us say a is not equal to x Okay, a is not equal to x and Then we can definitely say that a is equal to x plus m Isn't it a is equal to x plus m? So hence a and now we have a plus root b is equal to x plus root y and We can then say x plus m plus root b is equal to x plus root y Okay, so this x and this x goes so that means m Plus root b is equal to root y Which is impossible Impossible why Because on the left hand side we have our combination of rational plus irrational and on the right hand side We have an if a irrational only other way you can you can say m is equal to root y minus root b Now y and b are not perfect squares, right? are not perfect Squares we saw that above So that means what? That means what? root y minus root b is An irrational number is an irrational number Okay, and m being what a minus x was m. Isn't it from here see? M was a minus x which is difference of two rational number difference of two rational numbers hence hence M is a rational number m is a rational Number Right, therefore you're saying and an irrational number an Irrational number here if you see you are trying to equate an irrational number here in this step You're trying to equate an irrational number with a rational number. So any rational number cannot be cannot be equal to a Rational number isn't it? This is the fundamental Concept we have learned in irrational number will never be equal to a rational number hence our assumption hence our assumption our assumption that That x is not equal to a is wrong correct hence x must be equal to a and Now the moment x equals to a and then we had x plus root y is equal to a plus root b and Since x is equal to a so we can say root y is equal to root b and hence y is equal to b Right, so hence What is the conclusion? So conclusion a plus root b is equal to x plus root y if it is true where B and y must not be must not be Perfect Squires perfect Squires then a is equal to x and then a is equal to x and b equals y