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mgq--- 40 wgwbU m„Rbkxj cixÿv bs- 01 c~Y©gvb--- 30

cixÿv_©xi bvg:...................................................................................................... ‡ivj bst............................
[`ªóe¨: Wvb cv‡ki msL¨v cÖ‡kœi c~Y©gvb ÁvcK| ‡h †Kvb wZbwU cÖ‡kœi DËi `vI|]

ax2 + bx + c = 0

x
b= c=0 x1 x2

ax2 + bx + c = 0 a, b c a  0.
c=0
x1 x2
a = 1, b = c = 2p x1 x2

2
x + 8x + 16 = 0
a, b, c

ax2 + bx + c = 0

7x2  x  9 = 0

ax2 + bx + c = 0 a1 a2

a = 3, b = 4, c =  7
welq t D”PZi MwYZ---cÂg Aa¨vq GmGmwm cÖ¯‘wZ cixÿv- 2023 welq †KvW t 1 2 6
mgq--- 40 wgwbU m„Rbkxj cixÿv bs- 02 c~Y©gvb--- 30
cixÿv_©xi bvg:...................................................................................................... ‡ivj bst............................
[`ªóe¨: Wvb cv‡ki msL¨v cÖ‡kœi c~Y©gvb ÁvcK| ‡h †Kvb wZbwU cÖ‡kœi DËi `vI|]

ax2 + bx + c = 0

2x2  5x  1 = 0

a, b, c a0 ax2 + bx + c = 0

3  4x  x2 = 0 a, b, c

ax2 + bx + c = 0
c=0

2x2 + 7x  1 = 0

x2  6x = p
p = 16 x
p+9 p+6=1 x
p + 15  p + 13 = 10  8 x

11x  6 = 4x + 5  x  1
ax2 + bx + c = 0

x
welq t D”PZi MwYZ---cÂg Aa¨vq GmGmwm cÖ¯‘wZ cixÿv- 2023 welq †KvW t
1 2 6
mgq--- 40 wgwbU m„Rbkxj cixÿv bs- 03 c~Y©gvb--- 30
cixÿv_©xi bvg:...................................................................................................... ‡ivj bst............................
[`ªóe¨: Wvb cv‡ki msL¨v cÖ‡kœi c~Y©gvb ÁvcK| ‡h †Kvb wZbwU cÖ‡kœi DËi `vI|]

2 2
x  6x + 9  x  6x + 6 = 1
2
x  6x = y y+6 =1

x m
a1 a =a x=m

x x+4
3.27 = 9
mp 1 mp 2
3 = 3a (a > 0, a  3, p  0), m
x x 1
3(9  4.3 )+1=0

( 5 4) 4 x+7
= ( 11 64) 2 x+7
x x
a (a + b ) =
x
2 2
a b +1
2 2
ab
(a > 0, b > 0 ab  1)
m n
a =a

b = mx  1
x
m=1 b = 2 2
b b1
3 = 3.a x (a > 0, b  3, m  0)
2b b1
m=1 3  5.3  66 = 0 x

A. 3x.9y = 81
B. a3x + y.a2y = a20
C. 8yx  72x = 16
D. 2x = y2
B x >
A B (x, y)
C D
 welq t D”PZi MwYZ---cÂg Aa¨vq GmGmwm cÖ¯‘wZ cixÿv- 2023 welq †KvW t 1 2 6
mgq--- 40 wgwbU m„Rbkxj cixÿv bs- 04 c~Y©gvb--- 30
cixÿv_©xi bvg:...................................................................................................... ‡ivj bst............................
[`ªóe¨: Wvb cv‡ki msL¨v cÖ‡kœi c~Y©gvb ÁvcK| ‡h †Kvb wZbwU cÖ‡kœi DËi `vI|]

yx = x2  yx = 4 
 ; y  1
x2x = y4 y2 = 2x
x

2| (i) x2  xy = 14, y2 + xy = 60
x + y x  y 10 2 2
(ii) + = ,x y =3
x  y x+ y 3
2 2
(ii) x +y
(ii) (x, y)
(i)

4 4
3| (i) x + y = 1, y +
x
= 25
2 2 2 2
(ii) 2x + 3xy + y = 20, 5x + 4y = 41
(i) x y
(i) (x, y)
(ii)

10

600 x  15 = 0

12

108 21
welq t D”PZi MwYZ---cÂg Aa¨vq GmGmwm cÖ¯‘wZ cixÿv- 2023 welq †KvW t 1 2 6
mgq--- 40 wgwbU m„Rbkxj cixÿv bs- 05 c~Y©gvb--- 30
cixÿv_©xi bvg:...................................................................................................... ‡ivj bst............................
[`ªóe¨: Wvb cv‡ki msL¨v cÖ‡kœi c~Y©gvb ÁvcK| ‡h †Kvb wZbwU cÖ‡kœi DËi `vI|]

23 600

2 27
x y

56 20

300 10

10

10 600

2 2 25 15 10
 welq t D”PZi MwYZ---cÂg Aa¨vq GmGmwm cÖ¯‘wZ cixÿv- 2023 welq †KvW t 1 2 6
mgq--- 40 wgwbU m„Rbkxj cixÿv bs- 06 c~Y©gvb--- 30
cixÿv_©xi bvg:...................................................................................................... ‡ivj bst............................
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300 10 x y

x y

2| (i) 4p = 2q, (27)pq = 9q+1

qp 2p p
(ii) 18  q = 81, 3 = q2

i q p
i p q
ii

x
4 = 2y 
xy y + 1
(27) = 9 

x y
(1) 3 = 9
x+y+1 xy
(2) 5 = 25
x 2 x
(3) y = 4, y = 2
(1) x y
(1) (2) (x, y)
(3)

x 2 x
y =x  y =4 
2x 4 2 x y  1
x =y  y =2 
x