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IPMAT Indore 2024 - QA (SA) Q12 Explanation
November 22, 2024
Explanation:
(6) 4^log2𝑥−4𝑥+9^log3𝑦−16𝑦+68=0
⇒ 𝑥^log2 4−4𝑥+𝑦l^og39−16𝑦+68
⇒ 0 {Using property: a^logmx= x^logma}
⇒ 𝑥^2−4𝑥+𝑦^2−16𝑦+68 =0 {Using property: logxa^m= m.log𝑥𝑎 & logaa=1}
⇒ (𝑥^2−4𝑥+4)+(𝑦^2−16𝑦+64)
⇒ 0 {68 is splitted as 4+64}
⇒ (𝑥−2)^2+(𝑦−8)^2=0
The sum of two perfect squares equal to zero only possible if each term is zero.
∴(𝑥−2)^2=0 ⇒ 𝑥−2=0⇒𝑥=2
and (𝑦−8)^2=0 ⇒𝑦−8=0 ⇒𝑦=8
∴ y – x = 8 - 2 = 6. Ans