অষ্টম শ্রেণীর গণিত কষে দেখি (4.1)সমাধান
অষ্টম শ্রেণীর
গণিত
কষে দেখি (4.1)সমাধান
(a) অংকের সমস্যা টি সমাধান করা আছে।
(b) (x²+12-7y) (2x-y)
= 2x³ + 24x - 14xy - x²y - 12y + 7y²-
= x³ - x²y + 24x - 12y- 14xy + 7y²
x = -2, y = 2
= (-2)³ - (-2)2.2 + 24 (-2) - 12.2 - 14 (-2).2 + 7(2)²
= -8-8-48 - 24 +56 + 28 = 84 - 88 = -4
-
(c) (8p³ - 3p - 2p²) (4p² - 5)
= (8p³ - 2p²-3p) (4p²-5)
= 32p5 - 8p4 - 12p³ - 40p³ + 10p² +15p
= 32p5 - 8p⁴ - 52p³ + 10p² + 15p
= p (-2)
=32.(-2)5-8. (-2)4- 52.(-2)³ + 10(-2)² + 15.(-2)
= -1024 128 +416 + 40 - 30
= -1182 + 456 = -726
(d) (6a + 5b + 2) (a - b + 6)
= 6a² + 6ab +2a - 6ab- 5b²- 2b + 36a + 30b + 12
=6a²ab + 38a + 28b - 5b² + 12
a = 0, b = -1
= 6 × 0-0 × 6 + 38 x 0 + 28 (-1) - 5 (-1)² + 12
= -28 - 5 + 12
= -33 + 12 = - 21
(e) (p³ - p²q² + q³) (p² + pq + q²)
=P ³ -p⁴q³ + p²'q³ + p⁴'q-p³q³ + pq⁴ + p⁴q²
=p² + p⁴'q-p⁴q² - p³q³ + p³q² + p² q²
p²q⁴ + pq⁴+q 5
=p5 -p⁴q² + p⁴q -p³q³ + pq⁴ + p²q² - p²q⁴+q5
p=2,q=-2
=(2)5 (2)⁴. (-2)²+(2)⁴ (-2)- (2)³. (-2)³+2.(-
2)⁴+(2)²(-2)²-(-2)² (2)²(-2)⁴+(-2)5
=-32-64-32 +64 + 32 + 32-32-64-32
=-64
(f) (x² + y² + xz² - x²y - xyz - zx² + x⅜y
y³+ yz² - xy²-y²z - xyz + x²z + y²z+z xyz
--yz² - xz2
= x³+ y³+ z³ = 3xyz
x = 1, y = 0, z = -1
=(1)³+ (0)³ + (-1)³ - 3x1. × 0× -1
= -1-1=0
(g) ধরি দুটি বীজগাণিতিক সংখ্যা
= (x²+x + 1) (x²-x+1)
= (x²+1)²-(x)²
= x4+2x²+1-x²
= x4+x²+1
. = (-3)4+(-3)²+1
= 81+9+1
= 91
3. সরল করি :
1) (x+y) (x²-xy+y²) + (x−y) (x²+xy+y²)
প্রদত্ত রাশি
= (x+y) (x²-xy+y²) + (x−y) (x²+xy+y²)
= (x²-x²y + xy² + x²y - xy² + y) + (x³ + x²y + xy - x²y - xy²-y)
= x² + y² + x²-y³ = 2x³.
(ii) a² (b²-c²) + b²(c²-a²)+c²(a²-b²)
= (x+y) (x²-xy+y²) + (x-y) (x²+xy+y²)
= (x²-x²y + xy² + x²y-xy²+y³) + (x³ + x²y + xy²-x²y - xy² - y³)
= x³+y³+x³- y³
= 2x³
(ii) a² (b²-c²) + b² (c²-a²) + c²(a²-b²)
=a²b² - a²c² + b²c²-a²b²+ c²a²-b²c²
= 0
4. (i) a = x² + xy + y²,
b = y²+yz+z²,
c = x²+xz+x² হলে z²+xz+x²(x-y) a + (y-z) b+ (z-x) c এর মান নির্ণয় করি
সমাধান
4.(i) a = x²+xy+y², b = y²+yz+z², c = z²+xz+x²
= (x-y) a + (y-z) b+(z-x) c
= (x-y) (x²+xy+y²)+(y-z) (y²+yz+z²) + (z-x) (z²+xz+x²)
= (x³ + x²y + xy² - xy - xy²-y³) + (y³+y²z+yz-y'z-yz-2³) + (z²+z²x + zx² - 2²x-zx²-x³-
= (x³-y³) + (y³-z³) + (z³ - x³) = x³-y³+y³-z³ + z³ -x³ = 0
(ii) a = 1x + my + n, b = mx + ny+1, c = nx+1y+m হলে
, a (m+n) +b (n+1) +c (1+m)কী-হয় দেখি।
(ii) a lx+my + n, b = mx+ny+l, c = nx+ly+m
=
প্রদত্ত রাশি = a(m+n)+b(n+l)+c(I+m) = (Ix+my+n) (m+n)+(mn+ny+l) (n+l)+ (nx+ly+m) (I+m)
=lmx+m+y+mn+Inx+mny+a+mm+ny+In+Imn+Iny++Inx+y+im+mnx+Imy+m
- y (m+n+l+mn+In+Im) + 2x (Im+in+mn) + m+n+12+Im+In+mo