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Exercise 6.2, , Question 1:, Find the squares of the following numbers:, (i) 32, (ii) 35, (iii) 86, (iv) 93, (v) 71, (vi) 46, € Answer 1:, , (i) (32) =(30+ 2)" =(30)' +2x30x2+(2)° [+> (a+b)’ =a’ +2ab+b" |, = 900+ 120+4= 1024 :, (ii) 35)’ =(30+5)" =(30)' +2x30x5+(5)° [ (a+b)' =a? +2ab+8° |, = 900 + 300 + 25 = 1225 :, (iii) (86) =(80+6)' =(80)' +2x80x6+(6)' [+ (a+b)’ =a? +2ab+b" |, = 1600 + 960 + 36 = 7386 :, (iv) (93) =(90+3)' =(90)' +2x90x34(3)' [+ (a+b) =a? +2ab+b° |, = 8100 + 540 +9 = 8649 :, (v) (71) =(70+1)' =(70)' +2«70x1+(1)) [+s (a+b) =a? +2ab+b" |, = 4900 + 140 + 1=5041 :, , , , , , (vi) (46) =(40+6)° =(40)' +2x40x6+(6) [+ (a+b) =a? +2ab+b° |, = 1600 + 480 + 36 = 2116, , Question 2:, Write a Pythagoras triplet whose one member is:, (i) 6, (ii) 14, (iii) 16, (iv) 18, €. Answer 2:, (i) There are three numbers 2m,m* —1 and m’ +1 ina Pythagorean Triplet., Here, 2m=6 => m=o=3, Therefore,, , Second number (m? -1)=(3)' -1=9-1=8, , Third number m? +1=(3) +1=9+1=10, Hence, Pythagorean triplet is (6, 8, 10)., , , , ‘Scanned by CemScanner

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(ii), , (iii), , (iv), , There are three numbers 2m,m? —1 and m? +1 ina Pythagorean Triplet., Here, 2m=14, , => gulenl, 2, , Therefore,, Second number (m* -1)=(7) -1=49-1=48, , Third number nm? +1=(7) +1=49+1=50, Hence, Pythagorean triplet is (14, 48, 50)., There are three numbers 2m,m* —1 and m* +1 ina Pythagorean Triplet., Here, 2m=16, > m= am 8, 2, , Therefore,, Second number (m? -1) =(8)' -1=64-1=63, , Third number m? +1=(8)' +1=644+1=65, Hence, Pythagorean triplet is (16, 63, 65)., There are three numbers 2m,m* —1 and m’ +1 ina Pythagorean Triplet., Here, 2m=18, => m= us =f, 2, , Therefore,, Second number (m? =1)=(9) -1=81-1=80, , Third number m’? +1=(9)' +1=81+1=82, Hence, Pythagorean triplet is (18, 80, 82)., , ‘Scanned by CemScanner