CUET PG 2023 — Mathematics PYQ

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Question

CUET PG 2023 — Mathematics PYQ

CUET PG | Mathematics | 2023

The H.P. of two numbers is 4 and the arithmetic mean A and geometric mean G satisfy the relation 2A+G²=27. the numbers are

Choose the correct answer:

Explanation

Step 1: $G^2$ ki value replace karna

Diye gaye relation $2A + G^2 = 27$ mein hum $G^2 = AH$ substitute karenge:

2A + AH = 27

Kyunki $H = 4$ , equation hogi:

2A + 4A = 27

6A = 27

A = \frac{27}{6} = 4.5

Step 2: $G^2$ aur $A$ se product aur sum nikalna

Ab hum $G^2$ ki value nikalte hain:

G^2 = AH = 4.5 \times 4 = 18

Humein pata hai ki:

$A = \frac{a+b}{2} \implies a+b = 2A = 2 \times 4.5 = 9$
$G^2 = ab \implies ab = 18$

Step 3: Quadratic Equation banana

Aise do numbers jinka sum $9$ ho aur product $18$ ho, unke liye equation hogi:

x^2 - (a+b)x + ab = 0

x^2 - 9x + 18 = 0

Ab iske factors karte hain:

(x - 6)(x - 3) = 0

Isse humein milta hai:

x = 6 \quad \text{aur} \quad x = 3

Answer: Woh do numbers 6 aur 3 hain.