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Question Number 29887 by naka3546 last updated on 13/Feb/18

Commented by 803jaideep@gmail.com last updated on 13/Feb/18

$$1234?$$

Commented by naka3546 last updated on 13/Feb/18

$$areyousure?$$

Commented by 803jaideep@gmail.com last updated on 13/Feb/18

$$\mathrm{no}...\mathrm{i}\mathrm{just}\mathrm{guessed}\mathrm{from}\mathrm{the}\mathrm{series}$$$$\mathrm{answers}...\mathrm{i}\mathrm{dnt}\mathrm{knw}\mathrm{abt}\mathrm{it}$$

Answered by ajfour last updated on 13/Feb/18

$$a+4b+9c=16...\left(i\right)$$$$4a+9b+16c=25.....\left(ii\right)$$$$9a+16b+25c=36......\left(iii\right)$$$$andeven16a+25b+36c=49$$$$25a+36b+49c=64$$$$36a+49b+64c=81$$$$49a+64b+81c=100$$$$\left(iii\right)-\left(i\right)-\left(ii\right)gives$$$$4a+3b=-5.....\left(I\right)$$$$9\times \left(ii\right)-16\times \left(i\right)gives$$$$20a+17b=-31.....\left(II\right)$$$$\left(II\right)-5\times \left(I\right)gives$$$$2b=-6\Rightarrow b=-3$$$$thenfrom\left(I\right),$$$$4a-9=-5\Rightarrow a=1$$$$Andfrom\left(i\right),$$$$1-12+9c=16\Rightarrow c=3$$$$\Rightarrow l.h.s.ofeq.inquestion$$$$=1-3\left(12\right)+3\left(123\right)$$$$=334.$$

Commented by MJS last updated on 14/Feb/18

$$x^2-3{(x+1)}^2+3{(x+2)}^2={(x+3)}^2$$

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