(b) Given equations are
3[]1∕2+2[]1∕2 = 14
‌‌‌‌‌‌‌‌‌‌‌‌.......(i)
and
4[]1∕2−2[]1∕2 = 7
‌‌‌‌‌‌‌.......(ii)
Let
[]1∕2 = x and
[]1∕2 = y
Now , 3x + 2y = 14
‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌ ‌‌‌‌‌‌‌‌‌‌‌‌........(iii)
and
‌‌ 4x - 2y = 7
‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌........(iv)
On adding Eqs. (iii) and (iv) , we get
3x + 2y = 14
| 4x−2y=7 |
| −−−−−−−− |
‌‌‌‌‌‌ 7x = 21
∴
‌‌‌‌‌‌ x =
= 3
Now,
[]1∕2 = 3
On squaring both sides, we get
‌‌‌‌‌‌[]=32 ⇒ a = 9(b+1)
‌‌ ⇒ a - 9b = 9
‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌ .......(v)
Now, putting the value of x in Eq. (iii), we get
3x + 2y = 14 ⇒ 3 x 3 + 2y = 14
⇒ 2y = 14 - 9
∴
‌‌‌‌ y =
Now ,
[]1∕2=On squaring both sides, we get
‌‌‌‌‌[]=()2 ⇒
[]=⇒ 25a + 25 = 4b
⇒ 25a - 4b = - 25
‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌‌........(vi)
On multiplying Eq. (v) by 25 and then, subtracting Eq.(vi) from it, we get
25a - 225b = 225
25a - 4b = - 25
| +‌‌−‌‌‌‌‌+ |
| −−−−−−− |
- 221b = 250
∴ b =
On putting the value of b in Eq. (v), we get
a - 9
() = 9
⇒ a +
= 9
⇒ a = 9 -
= ∴ a =
and b =