If (9)^3 is subtracted from the square of a number, the answer so obtained is 567. What is the number?

Solution: By Euclid’s division algorithm, 693 = 567 x 1 + 126 567 = 126 x 4 + 63 126 = 63 x 2 + 0 So, HCF(441, 63) = 63 So, HCF (693, 567) =...

(i) The frog (ii) The Nightingale (iii) The speaker refers it as poor because she is dead (iv) She died when the veins of her neck bursted.

(i) Calpurnia is the speaker of the above lines. (ii) Calpurnia saw bad omens in her dream regarding Caesar. So, she is worried for him. (iii) Calpurnia is afraid for Caesar’s life...

(a) Let the the number be = x According o the question, x2 – 262 = 549 or, x2 – 676 = 549 or, x2 = 549 + 676 = 1225 or, x = √1225...

(b) Let the number be x. x2 + 612 = 5242 x2 = 5242 – 3721 = 1521 x = 39

(c) Let the number be x. Then, x2 – (74)2 = 5340 x2 = 5340 + 5476 = 10816 x = √10816 = 104

(d) Let the number be = x According to the question, x2 – (74)2 = 3740 or x2 = 3740 + 5476 = 9216 x = √9216 = 96

(b) Let the number be x x2 – (46)2 = 485 x2 = 485 + (46)2 = 2601 x = √2601 = 51

(e) Let the number be = x According to the question, x2 + 572 = 8010 or, x2 + 3249 = 8010 or, x2 = 8010 – 3249 = 4761 or, x = √4761 =...

(e) Let the number be x. According to the question, x2 – 782 = 6460 or, x2 = 6460 + 6084 or, x2 = 12544 or, x = √12544 = 112