Question

Directions (Q. Nos. 45-47) Four different integers
form an increasing AP. The largest number is equal
to the sum of the squares of the other three
numbers. Then,
45. The smallest number is
(a) - 2 (b) o
(c)-1 (d) 2​

Answer 1

Step-by-step explanation:

Let the numbers be a−d,a,a+d,a+2d

According to the hypothesis,

(a−d)

2

+a

2

+(a+d)

2

=a+2d

i.e 2d

2

−2d+3a

2

−a=0

∴d=

2

1

[1±

(1+2a−6a

2

)

]

Since, d is a positive integer,

1+2a−6a

2

>0

a

2

−

3

a

−

6

1

<0

(a−

6

1−

7

)(a−

6

1+

7

)<0

(

6

1−

7

)<a<(

6

1+

7

)

Since a is an integer,

∴a=0

then d=

2

1

[1±1]=1or0. Sinced>0∴d=1

Hence, the numbers are −1,0,1,