Menu Close

one-solution-of-the-equation-x-a-x-b-x-c-x-d-9-is-x-2-If-a-b-c-d-are-different-integers-then-a-b-c-d-

Tinku Tara 0 Comments
Pin




Question Number 196450 by cortano12 last updated on 25/Aug/23
one solution of the equation (x−a)(x−b)(x−c)(x−d) = 9 is x=2. If a,b,c,d are different integers then a+b+c+d =?
onesolutionoftheequation(x−a)(x−b)(x−c)(x−d)=9isx=2.Ifa,b,c,daredifferentintegersthena+b+c+d=?
Answered by Rasheed.Sindhi last updated on 25/Aug/23
(x−a)(x−b)(x−c)(x−d) = 9 x=2 x=2 (2−a)(2−b)(2−c)(2−d)=9 a,b,c,d are different integers ⇒2−a,2−b,2−c,2−d are different integers. • 9=1×−1×3×−3 [Order no matters] 2−a=1⇒a=1 2−b=−1⇒b=3 2−c=3⇒c=−1 2−d=−3⇒d=5 a+b+c+d=8✓
(x−a)(x−b)(x−c)(x−d)=9x=2x=2(2−a)(2−b)(2−c)(2−d)=9a,b,c,daredifferentintegers⇒2−a,2−b,2−c,2−daredifferentintegers.∙9=1×−1×3×−3[Ordernomatters]2−a=1⇒a=12−b=−1⇒b=32−c=3⇒c=−12−d=−3⇒d=5a+b+c+d=8✓
Answered by MM42 last updated on 25/Aug/23
let m=a+b+c+d & 2−a=p & 2−b=q & 2−c=r & 2−d=s ⇒m=8−(p+q+r+s) 1) p=1 , q=1 ,r=3 , s=3 ⇒m=0 × 2)p=−1 , q=−1 ,r=3 ,s=3 ⇒m=4 × 3)p=1 , q=1 ,r=−3 ,s=−3 ⇒m=12 × 4)p=1 , q=−1 ,r=3 ,s=−3 ⇒m=8 ✓ 5)p=−1 , q=−1 ,r=−3 ,s=−3 ⇒m=15 × 6)p=1 , q=1 ,r=1 ,s=9 ⇒m=−4 × 7)p=−1 , q=−1 ,r=1 ,s=9 ⇒m=0 × 8)p=1 , q=1 ,r=−1 ,s=−9 ⇒m=16 × 9)p=−1 , q=−1 ,r=−1 ,s=−9 ⇒m=20 ×
letm=a+b+c+d&2−a=p&2−b=q&2−c=r&2−d=s⇒m=8−(p+q+r+s)1)p=1,q=1,r=3,s=3⇒m=0×2)p=−1,q=−1,r=3,s=3⇒m=4×3)p=1,q=1,r=−3,s=−3⇒m=12×4)p=1,q=−1,r=3,s=−3⇒m=8✓5)p=−1,q=−1,r=−3,s=−3⇒m=15×6)p=1,q=1,r=1,s=9⇒m=−4×7)p=−1,q=−1,r=1,s=9⇒m=0×8)p=1,q=1,r=−1,s=−9⇒m=16×9)p=−1,q=−1,r=−1,s=−9⇒m=20×
Answered by mr W last updated on 25/Aug/23
say a<b<c<d (a−2)(b−2)(c−2)(d−2)=9 let p=a−2, q=b−2, r=c−2, s=d−2 a+b+c+d=p+q+r+s+8 pqrs=9 with p<q<r<s only one possibility: pqrs=(−3)(−1)(1)(3)=9 ⇒a+b+c+d=−3−1+1+3+8=8 ✓
saya<b<c<d(a−2)(b−2)(c−2)(d−2)=9letp=a−2,q=b−2,r=c−2,s=d−2a+b+c+d=p+q+r+s+8pqrs=9withp<q<r<sonlyonepossibility:pqrs=(−3)(−1)(1)(3)=9⇒a+b+c+d=−3−1+1+3+8=8✓
Commented by MM42 last updated on 25/Aug/23
you are right.i did no pay attention to the difference in number Thank you sir.
youareright.ididnopayattentiontothedifferenceinnumberThankyousir.

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *