 Hello and welcome to the session. In this session we discussed the following question which says if A upon B is equal to C upon D is equal to E upon F show that each ratio is equal to 3A square plus 5C square minus 7E square this whole upon 3B square plus 5D square minus 7S square this whole to the power 1 upon 2. Let's move on to the solution now we are given that A upon B is equal to C upon D is equal to E upon F we assume let A upon B is equal to C upon D is equal to E upon F be equal to K that is we have assumed each ratio to be equal to K then we say A is equal to BK since we have assumed A upon B to be equal to K so this gives us A is equal to BK in the same way we get C is equal to DK then E is equal to FK. Let us now consider the expression 3A square plus 5C square minus 7E square this whole upon 3B square plus 5D square minus 7F square and this whole to the power 1 upon 2. Now since we are supposed to show that each of the given ratios is equal to this given expression so if we show that this given expression is equal to K then this would mean that each given ratio is equal to this expression since we have assumed each of the given ratios is equal to K. So let us now try to show this expression equal to K so in this expression we would substitute A as BK so this would be equal to 3 into B square K square plus now in place of C we would put BK so here we would have 5D square K square minus in place of E we would put FK so here we have minus 7F square K square and this whole upon 3B square plus 5D square minus 7F square and this whole to the power of 1 upon 2. Now we take K square common from the numerator so inside the brackets we are left with 3B square plus 5D square minus 7F square and this whole upon 3B square plus 5D square minus 7F square and this whole to the power of 1 upon 2. Now 3B square plus 5D square minus 7F square cancels with 3B square plus 5D square minus 7F square and so here we are left with K square whole to the power of 1 upon 2 this means we get this equal to K therefore here we have 3A square plus 5C square minus 7E square this whole upon 3B square plus 5D square minus 7F square this whole to the power of 1 upon 2 is equal to K and since we had assumed each ratio that is A upon B is equal to C upon D is equal to E upon F equal to K therefore we can say that A upon B is equal to C upon D is equal to E upon F is equal to 3A square plus 5C square minus 7E square this whole upon 3B square plus 5D square minus 7F square this whole to the power of 1 upon 2 so each ratio is equal to this expression so hence proved this completes the session hope you have understood the solution of this question.