Question

17. If a - b=4 and ab = 21 then find the value a - 63​

Answer 1

Answer:

a - 63 = -56, - 66

Step-by-step explanation:

As a - b = 4,

so, a = b+4

Now, ab = 21

=> (b+4)b = 21

$=> b^2 + 4b = 21\\=> b^2 + 2.b.2 + 2^2 = 21 + 2^2\\=> (b+2)^2 = 25\\=> b+2 = 5, -5\\=> b = 3, -7$

when, b = 3 then a = 3+4 = 7 => a - 63 = 7 - 63 = -56

and

when, b = -7 then a = -7+4 = -3 => a - 63 = -3 - 63 = -66

Answer 2

value a - 63​ can be -66 or -56  If a - b=4 and ab = 21

Given:

• a - b = 4
• ab = 21

To Find:

• Value of a - 63

Solution:

Step 1:

Isolate b

a - b = 4

=> a - 4 = b

Step 2:

Substitute b = a - 4 in ab = 21

a(a - 4) = 21

Step 3:

Solve for a

a² -4a = 21

a² - 4a - 21 = 0

a² - 7a + 3a - 21 = 0

a(a - 7) + 3(a - 7) =0

(a + 3)(a - 7) = 0

=> a = -3 , a = 7

Step 4:

Calculate a - 63

-3 - 63 = -66

7 - 63 = -56

Hence the value a - 63​ can be -66 or -56

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