代数表达式
NCERT练习9.5
第2部分
问题5:证明一下。
(我)' (3x + 7)²- 84x = (3x - 7)²'
答:LHS ' = 9x^2 + 42x + 49 - 84x '
' = 9x^2- 42x + 49 '
RHS ' = 9x^2 - 42x + 49 '
' lhs = rhs '
(2)' (9p - 5q)²+ 180pq = (9p + 5q)²'
答:LHS ' = 81p^2 - 90pq + 25q^2+ 180pq '
' = 81p²+ 90pq + 25q²'
RHS ' = 81p^2 + 90pq + 25q^2 '
(3)”(4/3m-3/4n) ^ 2 + 2 mn = (16) / (9) m ^ 2 + (9) / (16) n ^ 2”
答:”(16)/ (9)m ^ 2 + (9) / (16) n ^ 2-2mn + 2 mn的
证明' =(16)/(9)m²+(9)/(16)n²' = RHS
(iv)' (4pq + 3q)²- (4pq - 3q)²= 48pq²'
答:' = 16p^2q²+ 24pq²+ 9q²- 16p^2q²+ 24pq²- 9q²'
“= 48 pq ^ 2”
(v)”(a - b) (a + b) + (b - c) (b + c) + (c - a) (c + a) = 0的
答:' = a^2 - b^2 + b^2 - c^2 + c^2 - a^2= 0 '
问题6:使用身份，评估。
(我)“71 ^ 2”
答:' 71^2 = (70+1)^2 '
使用' (a + b)²= a²+ 2ab + b²'
' = 70²+ 140 + 1²'
' = 4900 + 140 +1= 5041 '
(2)“99 ^ 2”
答:' =(100 -1)²'
= 100^2 - 200 + 1^2 '
' = 10000 - 200 + 1= 9801 '
(3)“102 ^ 2”
答:= (100 + 2)^2 '
' = 100²+ 400 + 2²'
' = 10000 + 400 + 4= 10404 '
(iv)“998 ^ 2”
答:= (1000 - 2)^2 '
' = 1000²- 4000 + 2²'
' = 1000000 - 4000 + 4= 996004 '
(v)“5.2 ^ 2”
答:' = (5 + 0.2)^2 '
' = 5²+ 2 + 0.2²'
' = 25 + 2 + 0.4= 27.4 '
(vi)' 297 xx 303 '
答:' = (300 - 3) (300 + 3) '
使用' (a - b)(a + b) = a^2 - b^2 '
= 300^2 - 3^2 '
' = 90000 - 9= 89991 '
(七)' 78 xx 82 '
答:= (80 - 2)(80 + 2) '
' = 80²- 2²'
' = 6400 - 4= 6396 '
(八)“8.9 ^ 2”
答:' = (9 - 0.1)^2 '
= 9^2 - 1.8 + 0.1^2 '
' = 81 - 1.8 + 0.01= 79.21 '
(第九)' 10.5 xx 9.5 '
答:' = (10 + 0.5)(10 - 0.5) '
= 10^2 - 0.5^2 '
' = 100 - 0.25= 99.75 '
问题7:用' a^2 - b^2 = (a + b) (a - b) '求
(我)《51 ^ 2 - 49 ^ 2》
答:' = (51 + 49)(51 - 49) '
' = 100 xx 2= 200 '
(2)”(1.02)^ 2 -(0.98)^ 2》
答:' = (1.02 + 0.98)(1.02 - 0.98) '
' = 2 xx 0.04= 0.08 '
(3)153 ^ 2 - 147 ^ 2
答:' = (153 + 147)(153 - 147) '
= 300 xx 6= 1800 '
(iv)“12.1 7.9 ^ ^ 2 - 2”
答:' = (12.1 + 7.9)(12.1 - 7.9) '
' = 20 xx 4.2= 84 '
问题8:用' (x + a) (x + b) = x^2+ (a + b) x + ab '求
(我)' 103 xx 104 '
答:= (100 + 3)(100 + 4) '
' = 100^2 + (3 + 4)100 + 12 '
' = 10000 + 1200 + 12= 11212 '
(2)' 5.1 xx 5.2 '
答:' = (5 + 0.1)(5 + 0.2) '
' = 5^2 + (0.1+0.2)5 + 0.02 '
' = 25 + 1.5 + 0.02= 26.52 '
(3)' 103 xx 98 '
回答' = (100 + 3)(100 - 2) '
' = 100^2 + (3-2)100 - 6 '
' = 10000 + 100 - 6= 10094 '
(iv)' 9.7 xx 9.8 '
答:' = (9 + 0.7)(9 + 0.8) '
' = 9^2 + (0.7 + 0.8)9 + 0.63 '
' = 81 + 13.5 + 0.63= 95.13 '